Question 1

Determine whether the graph is that of a function. If it is, use the graph to find its domain and range, the intercepts, if any, and any symmetry with respect to the x-axis, the y-axis, or the origin.
-
A) function
domain: {x|-7 ≤ x ≤7} 
Range: {y|-7 ≤ y ≤ 7} 
Intercepts: (-7, 0), (0, -7), (0, 0), (0, 7), (7, 0) 
Symmetry: origin

B) function 
domain: {x|-7 ≤ x ≤7}
range: {y|-7 ≤ y ≤ 7}
intercepts: (-7, 0), (0, -7), (0, 7), (7, 0)
symmetry: x-axis, y-axis, origin

C) function
domain: {x|-7 ≤ x ≤7}
Range: {y|-7 ≤ y ≤ 7}
Intercepts: (-7, 0), (0, -7), (0, 7), (7, 0)
Symmetry: x-axis, y-axis

D) not a function

Accepted Answer

The answer of Determine whether the graph is that of...

Question 2

Solve the problem.
-$\text { Given } f ( x ) = \frac { 1 } { x } \text { and } \left( \frac { f } { g } \right) ( x ) = \frac { x - 4 } { x ^ { 2 } - 6 x } \text {, find the function } g \text {. }$
A) $g ( x ) = \frac { x + 4 } { x + 6 }$
B) $g ( x ) = \frac { x + 6 } { x + 4 }$
C) $g ( x ) = \frac { x - 4 } { x - 6 }$
D) $g ( x ) = \frac { x - 6 } { x - 4 }$

Accepted Answer

Given $\left( \frac { f } { g } \right) ( x ) = \frac { x - 4 } { x ^ { 2 } - 6 x }$ and $f(x) = \frac{1}{x}$, we find $g(x)$ by rearranging the equation: $g(x) = \frac{f(x)}{\left( \frac { f } { g } \right) ( x )}$. Substituting $f(x) = \frac{1}{x}$ and $\left( \frac { f } { g } \right) ( x ) = \frac { x - 4 } { x ^ { 2 } - 6 x }$, we get $g(x) = \frac{x(x^2 - 6x)}{x-4}$. Simplifying, $g(x) = \frac{x^2 - 6x}{x-4}$, which can be further simplified to $g(x) = \frac{x(x - 6)}{x-4}$, matching choice D.

Question 3

For the given functions f and g, find the requested function and state its domain.
-$f ( x ) = \sqrt { x } ; g ( x ) = 5 x - 8$
Find $\frac { \mathrm { f } } { \mathrm { g } }$. 
A) $\left( \frac { f } { g } \right) ( x ) = \frac { 5 x - 8 } { \sqrt { x } } ; \{ x \mid x \geq 0 \}$
B) $\left( \frac { f } { g } \right) ( x ) = \frac { \sqrt { x } } { 5 x - 8 } ; \left\{ x \mid x \geq 0 , x \neq \frac { 8 } { 5 } \right\}$
C) $\left( \frac { \mathrm { f } } { \mathrm { g } } \right) ( \mathrm { x } ) = \frac { \sqrt { \mathrm { x } } } { 5 \mathrm { x } - 8 } ; \left\{ \mathrm { x } \mid \mathrm { x } \neq \frac { 8 } { 5 } \right\}$
D) $\left( \frac { f } { g } \right) ( x ) = \frac { \sqrt { x } } { 5 x - 8 } ; \{ x \mid x \neq 0 \}$

Accepted Answer

The division of $f$ by $g$ gives $\frac{\sqrt{x}}{5x-8}$. The domain includes $x \geq 0$ because of the square root in the numerator, and excludes $x = \frac{8}{5}$ because it makes the denominator zero.

Question 4

Determine whether the graph is that of a function. If it is, use the graph to find its domain and range, the intercepts, if any, and any symmetry with respect to the x-axis, the y-axis, or the origin.
-
A) function
domain: {x|-2 ≤ x ≤2} 
Range: all real numbers 
Intercepts: (-2, 0), (2, 0) 
Symmetry: x-axis, y-axis

B) function
 domain: all real numbers
range: {y|y ≤-2 or y ≥ 2}
intercepts: (-2, 0), (2, 0)
symmetry: y-axis

C) function
domain: {x|x ≤-2 or x ≥ 2}
Range: all real numbers
Intercepts: (-2, 0), (2, 0)
Symmetry: x-axis, y-axis, origin

D) not a function

Accepted Answer

The answer of Determine whether the graph is that of...

Question 5

For the given functions f and g, find the requested function and state its domain.
-$\begin{array} { l } 
f ( x ) = x + 6 ; g ( x ) = 3 x ^ { 2 } \  { Find } f + g
\end{array}$ 
A) $( f + g ) ( x ) = - 3 x ^ { 2 } + x + 6$; all real numbers
B) $( f + g ) ( x ) = 3 x ^ { 2 } - x - 6 ;$ all real numbers
C) $( f + g ) ( x ) = 3 x ^ { 2 } + x + 6 ; \{ x \mid x \neq - 6 \}$
D) $( f + g ) ( x ) = 3 x ^ { 2 } + x + 6$; all real numbers

Accepted Answer

To find $f + g$, you add the functions $f(x) = x + 6$ and $g(x) = 3x^2$ together, resulting in $3x^2 + x + 6$. Both functions are polynomials, which are defined for all real numbers, so the domain of $f + g$ is all real numbers.

Question 6

Find and simplify the difference quotient of f $\frac { f ( x + h ) - f ( x ) } { h }$ , h ≠ 0, for the function.
-f(x) = 4x - 2
A) 0 
B) $4 + \frac { - 4 } { h }$
C) $4 + \frac { 8 ( x - 2 ) } { h }$
D) 4

Accepted Answer

The difference quotient for the function $f(x) = 4x - 2$ is calculated as follows: $\frac{f(x+h) - f(x)}{h} = \frac{(4(x+h) - 2) - (4x - 2)}{h} = \frac{4x + 4h - 2 - 4x + 2}{h} = \frac{4h}{h} = 4$. This simplifies to 4, indicating that the rate of change of the function is constant.

Question 7

For the given functions f and g, find the requested function and state its domain.
-f(x) = 5x + 4; g(x) = 5x - 3 $\text { Find } \frac { \mathrm { f } } { \mathrm { g } } \text {. }$ 
A) $\left( \frac { \mathrm { f } } { \mathrm { g } } \right) ( \mathrm { x } ) = \frac { 5 \mathrm { x } - 3 } { 5 \mathrm { x } + 4 } ; \left\{ \mathrm { x } \mid \mathrm { x } \neq \frac { 3 } { 5 } \right\}$
B) $\left( \frac { f } { g } \right) ( x ) = \frac { 5 x - 3 } { 5 x + 4 } ; \left\{ x \mid x \neq - \frac { 4 } { 5 } \right\}$
C) $\left( \frac { f } { g } \right) ( x ) = \frac { 5 x + 4 } { 5 x - 3 } ; \left\{ x \mid x \neq \frac { 3 } { 5 } \right\}$
D) $\left( \frac { \mathrm { f } } { \mathrm { g } } \right) ( \mathrm { x } ) = \frac { 5 \mathrm { x } + 4 } { 5 \mathrm { x } - 3 } ; \left\{ \mathrm { x } \mid \mathrm { x } \neq - \frac { 4 } { 5 } \right\}$

Accepted Answer

The answer of For the given functions f and g,...

Question 8

For the given functions f and g, find the requested function and state its domain.
-$f ( x ) = \sqrt { x + 13 } ; g ( x ) = \frac { 4 } { x }$ Find f · g. 
A) $( f \cdot g ) ( x ) = \frac { \sqrt { 4 x + 52 } } { x } ; \{ x \mid x \geq - 13 , x \neq 0 \}$
B) $( f \cdot g ) ( x ) = \sqrt { \frac { 17 } { x } } ; \{ x \mid x \neq 0 \}$
C) $( f \cdot g ) ( x ) = \frac { 4 \sqrt { x + 13 } } { x } ; \{ x \mid x \geq - 13 , x \neq 0 \}$
D) $( f \cdot g ) ( x ) = \sqrt { \frac { 4 x + 52 } { x } } ; \{ x \mid x \geq - 13 , x \neq 0 \}$

Accepted Answer

The product $f \cdot g$ is found by multiplying $f(x) = \sqrt{x + 13}$ and $g(x) = \frac{4}{x}$ together, resulting in $\frac{4\sqrt{x + 13}}{x}$. The domain is $x \geq -13$ to ensure the radicand is non-negative and $x \neq 0$ to avoid division by zero.

Question 9

Solve the problem.
-Suppose that P(x) represents the percentage of income spent on housing in year x and I(x) represents income in year x. Determine a function H that represents total housing expenditures in year x.
A) H(x) = (P · I)(x)
B) H(x) = (P + I)(x)
C) $$\mathrm { H } ( \mathrm { x } ) = \left( \frac { \mathrm { I } } { \mathrm { P } } \right) ( \mathrm { x } )$$
D) H(x) = (I - P)(x)

Accepted Answer

H(x) = (P · I)(x) correctly represents total housing expenditures in year x because it multiplies the percentage of income spent on housing (P(x)) by the income (I(x)) to get the total amount spent on housing.

Question 10

Solve the problem.
-A retail store buys 225 VCRs from a distributor at a cost of $205 each plus an overhead charge of $20 per order. The retail markup is 40% on the total price paid. Find the profit on the sale of one VCR.
A) $82.04
B) $82.00
C) $8204.00
D) $81.96

Accepted Answer

The cost of one VCR for the store is $205 plus the overhead charge of $20 per order, divided by the number of VCRs, which is negligible when divided by 225. So, the cost is approximately $205. The retail price is $205 * 1.40 = $287. The profit on one VCR is $287 - $205 = $82.

Question 11

Find and simplify the difference quotient of f $\frac { f ( x + h ) - f ( x ) } { h }$ , h ≠ 0, for the function.
-$( x ) = \frac { 1 } { 7 x }$ 
A) $\frac { - 1 } { x ( x + h ) }$
B) $\frac { 1 } { 7 x }$
C) 0
D) $\frac { - 1 } { 7 x ( x + h ) }$

Accepted Answer

The difference quotient for the function $f(x) = \frac{1}{7x}$ is calculated as follows: $\frac{f(x+h)-f(x)}{h} = \frac{\frac{1}{7(x+h)} - \frac{1}{7x}}{h}$. Simplifying this expression leads to $\frac{-1}{7x(x+h)}$, which matches choice D.

Question 12

Find and simplify the difference quotient of f $\frac { f ( x + h ) - f ( x ) } { h }$ , h ≠ 0, for the function.
-$$f ( x ) = x ^ { 2 } + 6 x - 8$$
A) 2x+ h - 8
B) $$\frac { 2 x ^ { 2 } + 2 x + 2 x h + h ^ { 2 } + h - 16 } { h }$$
C) 1
D) 2x+ h + 6

Accepted Answer

The difference quotient for the function $f(x) = x^2 + 6x - 8$ is found by substituting $f(x + h)$ and $f(x)$ into the formula $\frac{f(x + h) - f(x)}{h}$. First, find $f(x + h)$:$$f(x + h) = (x + h)^2 + 6(x + h) - 8$$$$= x^2 + 2xh + h^2 + 6x + 6h - 8$$Then, subtract $f(x)$ from $f(x + h)$:$$f(x + h) - f(x) = (x^2 + 2xh + h^2 + 6x + 6h - 8) - (x^2 + 6x - 8)$$$$= 2xh + h^2 + 6h$$Finally, divide by $h$ (and assuming $h \neq 0$):$$\frac{f(x + h) - f(x)}{h} = \frac{2xh + h^2 + 6h}{h}$$$$= 2x + h + 6$$Therefore, the correct answer is 2x + h + 6, which matches choice D.

Question 13

Solve the problem.
-Express the gross salary G of a person who earns $40 per hour as a function of the number x of hours worked. 
A) $G ( x ) = \frac { 40 } { x }$
B) $G ( x ) = 40 x ^ { 2 }$
C) $G ( x ) = 40 x$
D) $G ( x ) = 40 + x$

Accepted Answer

The gross salary (G) is directly proportional to the number of hours worked (x), with a rate of $40 per hour, so the correct expression is $G(x) = 40x$.

Question 14

For the given functions f and g, find the requested function and state its domain.
-$f ( x ) = \sqrt { 7 - x } ; g ( x ) = \sqrt { x - 3 }$
Find $f \cdot g$. 
A) $( f \cdot g ) ( x ) = \sqrt { ( 7 - x ) ( x - 3 ) } ; \{ x \mid x \geq 0 \}$
B) $( f \cdot g ) ( x ) = \sqrt { ( 7 - x ) ( x - 3 ) } ; \{ x \mid x \neq 3 , x \neq 7 \}$
C) $( f \cdot g ) ( x ) = \sqrt { - x ^ { 2 } - 21 } ; \{ x \mid x \neq 21 \}$
D) $( f \cdot g ) ( x ) = \sqrt { ( 7 - x ) ( x - 3 ) } ; \{ x \mid 3 \leq x \leq 7 \}$

Accepted Answer

The product of $f(x)$ and $g(x)$ is indeed $\sqrt{(7-x)(x-3)}$. The domain of this function is determined by the conditions that $7-x \geq 0$ and $x-3 \geq 0$, which simplify to $x \leq 7$ and $x \geq 3$, respectively. Therefore, the domain is $\{x \mid 3 \leq x \leq 7\}$.

Question 15

For the given functions f and g, find the requested function and state its domain.
-$f ( x ) = 16 - x ^ { 2 } ; g ( x ) = 4 - x$
Find $f + g$. 
A) $( f + g ) ( x ) = - x ^ { 2 } - x + 20 ; \{ x \mid x \neq 4 , x \neq - 5 \}$
B) $( f + g ) ( x ) = 4 + x ; \{ x \mid x \neq - 4 \}$
C) $( f + g ) ( x ) = - x ^ { 2 } + x + 12 ;$ all real numbers
D) $( f + g ) ( x ) = x ^ { 3 } - 4 x ^ { 2 } - 16 x + 64$; all real numbers

Accepted Answer

The answer of For the given functions f and g,...

Question 16

Determine whether the graph is that of a function. If it is, use the graph to find its domain and range, the intercepts, if any, and any symmetry with respect to the x-axis, the y-axis, or the origin.
-
A) function
domain: all real numbers 
Range: {y|y > 0} 
Intercept: (1, 0) 
Symmetry: none

B) function 
domain: {x|x > 0}
range: all real numbers
intercept: (0, 1)
symmetry: origin

C) function
domain: {x|x > 0}
Range: all real numbers
Intercept: (1, 0)
Symmetry: none

D) not a function

Accepted Answer

The answer of Determine whether the graph is that of...

Question 17

Determine whether the graph is that of a function. If it is, use the graph to find its domain and range, the intercepts, if any, and any symmetry with respect to the x-axis, the y-axis, or the origin.
-
A) function
domain: all real numbers 
Range: {y|y ≤9} 
Intercepts: (0, -4), (8, 0), (0, 2) 
Symmetry: none

B) function 
domain: {x|x ≤9}
range: all real numbers
intercepts: (-4, 0), (0, 8), (2, 0)
symmetry: y-axis

C) function
domain: all real numbers
Range: {y|y ≤9}
Intercepts: (-4, 0), (0, 8), (2, 0)
Symmetry: none

D) not a function

Accepted Answer

The answer of Determine whether the graph is that of...

Question 18

For the given functions f and g, find the requested function and state its domain.
-$f ( x ) = 5 x ^ { 3 } - 2 ; g ( x ) = 5 x ^ { 2 } + 3$
Find $f \cdot g$. 
A) $( f \cdot g ) ( x ) = 5 x ^ { 3 } + 5 x ^ { 2 } - 6$; all real numbers
B) $( f \cdot g ) ( x ) = 25 x ^ { 6 } + 15 x ^ { 3 } - 10 x ^ { 2 } - 6$; all real numbers
C) $( f \cdot g ) ( x ) = 25 x ^ { 5 } + 15 x ^ { 3 } - 10 x ^ { 2 } - 6$; all real numbers
D) $( f \cdot g ) ( x ) = 25 x ^ { 5 } + 15 x ^ { 3 } - 10 x ^ { 2 } - 6 ; \{ x \mid x \neq 0 \}$

Accepted Answer

The product $f \cdot g$ is found by multiplying the functions: $(5x^3 - 2)(5x^2 + 3) = 25x^5 + 15x^3 - 10x^2 - 6$. The domain is all real numbers since there are no restrictions from division or square roots.

Question 19

For the given functions f and g, find the requested function and state its domain.
-$f ( x ) = \frac { 5 x - 8 } { 9 x - 2 } ; g ( x ) = \frac { 3 x } { 9 x - 2 }$ Find f - g. 
A) $( f - g ) ( x ) = \frac { 2 x - 8 } { 9 x - 2 } ; \left\{ x \mid x \neq \frac { 2 } { 9 } , x \neq 4 \right\}$
B) $( f - g ) ( x ) = \frac { 2 x - 8 } { 9 x - 2 } ; \left\{ x \mid x \neq \frac { 2 } { 9 } \right\}$
C) $( \mathrm { f } - \mathrm { g } ) ( \mathrm { x } ) = \frac { 8 \mathrm { x } + 8 } { 9 \mathrm { x } - 2 } ; \left\{ \mathrm { x } \mid \mathrm { x } \neq \frac { 2 } { 9 } \right\}$
D) $( f - g ) ( x ) = \frac { 2 x - 8 } { 9 x - 2 } ; \{ x \mid x \neq 0 \}$

Accepted Answer

To find $f - g$, subtract $g(x)$ from $f(x)$: $f(x) - g(x) = \frac{5x - 8}{9x - 2} - \frac{3x}{9x - 2} = \frac{5x - 8 - 3x}{9x - 2} = \frac{2x - 8}{9x - 2}$. The domain excludes values that make the denominator zero, which is only $x = \frac{2}{9}$.

Question 20

Solve the problem.
-Jacey, a commissioned salesperson, earns $180 base pay plus $47 per item sold. Express Jacey's gross salary G as a function of the number x of items sold. 
A) $G ( x ) = 180 x + 47$
B) $G ( x ) = 47 ( x + 180 )$
C) $G ( x ) = 180 ( x + 47 )$
D) $G ( x ) = 47 x + 180$

Accepted Answer

Jacey's gross salary $G$ consists of a fixed base pay of $180 plus $47 for each item sold. Therefore, for $x$ items sold, the salary is $47x + 180$, making option D correct.

Quiz 1: Functions and Their Graphs

Determine whether the graph is that of a function. If it is, use the graph to find its domain and range, the intercepts, if any, and any symmetry with respect to the x-axis, the y-axis, or the origin. -

Solve the problem. - $\text { Given } f ( x ) = \frac { 1 } { x } \text { and } \left( \frac { f } { g } \right) ( x ) = \frac { x - 4 } { x ^ { 2 } - 6 x } \text {, find the function } g \text {. }$

For the given functions f and g, find the requested function and state its domain. - $f ( x ) = \sqrt { x } ; g ( x ) = 5 x - 8$ Find $\frac { \mathrm { f } } { \mathrm { g } }$ .

Determine whether the graph is that of a function. If it is, use the graph to find its domain and range, the intercepts, if any, and any symmetry with respect to the x-axis, the y-axis, or the origin. -

For the given functions f and g, find the requested function and state its domain. - $\begin{array} { l } f ( x ) = x + 6 ; g ( x ) = 3 x ^ { 2 } \\ { Find } f + g\end{array}$

Find and simplify the difference quotient of f $\frac { f ( x + h ) - f ( x ) } { h }$ , h ≠ 0, for the function. -f(x) = 4x - 2

For the given functions f and g, find the requested function and state its domain. -f(x) = 5x + 4; g(x) = 5x - 3 $\text { Find } \frac { \mathrm { f } } { \mathrm { g } } \text {. }$

For the given functions f and g, find the requested function and state its domain. - $f ( x ) = \sqrt { x + 13 } ; g ( x ) = \frac { 4 } { x }$ Find f · g.

Solve the problem. -Suppose that P(x) represents the percentage of income spent on housing in year x and I(x) represents income in year x. Determine a function H that represents total housing expenditures in year x.

Solve the problem. -A retail store buys 225 VCRs from a distributor at a cost of $205 each plus an overhead charge of $20 per order. The retail markup is 40% on the total price paid. Find the profit on the sale of one VCR.

Find and simplify the difference quotient of f $\frac { f ( x + h ) - f ( x ) } { h }$ , h ≠ 0, for the function. - $( x ) = \frac { 1 } { 7 x }$

Find and simplify the difference quotient of f $\frac { f ( x + h ) - f ( x ) } { h }$ , h ≠ 0, for the function. - $f ( x ) = x ^ { 2 } + 6 x - 8$

Solve the problem. -Express the gross salary G of a person who earns $40 per hour as a function of the number x of hours worked.

For the given functions f and g, find the requested function and state its domain. - $f ( x ) = \sqrt { 7 - x } ; g ( x ) = \sqrt { x - 3 }$ Find $f \cdot g$ .

For the given functions f and g, find the requested function and state its domain. - $f ( x ) = 16 - x ^ { 2 } ; g ( x ) = 4 - x$ Find $f + g$ .

Determine whether the graph is that of a function. If it is, use the graph to find its domain and range, the intercepts, if any, and any symmetry with respect to the x-axis, the y-axis, or the origin. -

Determine whether the graph is that of a function. If it is, use the graph to find its domain and range, the intercepts, if any, and any symmetry with respect to the x-axis, the y-axis, or the origin. -

For the given functions f and g, find the requested function and state its domain. - $f ( x ) = 5 x ^ { 3 } - 2 ; g ( x ) = 5 x ^ { 2 } + 3$ Find $f \cdot g$ .

For the given functions f and g, find the requested function and state its domain. - $f ( x ) = \frac { 5 x - 8 } { 9 x - 2 } ; g ( x ) = \frac { 3 x } { 9 x - 2 }$ Find f - g.

Solve the problem. -Jacey, a commissioned salesperson, earns $180 base pay plus $47 per item sold. Express Jacey's gross salary G as a function of the number x of items sold.

Quiz 1: Functions and Their Graphs

Determine whether the graph is that of a function. If it is, use the graph to find its domain and range, the intercepts, if any, and any symmetry with respect to the x-axis, the y-axis, or the origin. -

For the given functions f and g, find the requested function and state its domain. - f(x) =x;g(x) =5x−8f ( x ) = \sqrt { x } ; g ( x ) = 5 x - 8f(x) =x​;g(x) =5x−8 Find fg\frac { \mathrm { f } } { \mathrm { g } }gf​ .

Determine whether the graph is that of a function. If it is, use the graph to find its domain and range, the intercepts, if any, and any symmetry with respect to the x-axis, the y-axis, or the origin. -

For the given functions f and g, find the requested function and state its domain. - f(x) =x+6;g(x) =3x2Findf+g\begin{array} { l } f ( x ) = x + 6 ; g ( x ) = 3 x ^ { 2 } \\ { Find } f + g\end{array}f(x) =x+6;g(x) =3x2Findf+g​

Find and simplify the difference quotient of f f(x+h) −f(x) h\frac { f ( x + h ) - f ( x ) } { h }hf(x+h) −f(x) ​ , h ≠ 0, for the function. -f(x) = 4x - 2

For the given functions f and g, find the requested function and state its domain. -f(x) = 5x + 4; g(x) = 5x - 3 Find fg. \text { Find } \frac { \mathrm { f } } { \mathrm { g } } \text {. } Find gf​.

For the given functions f and g, find the requested function and state its domain. - f(x) =x+13;g(x) =4xf ( x ) = \sqrt { x + 13 } ; g ( x ) = \frac { 4 } { x }f(x) =x+13​;g(x) =x4​ Find f · g.

Solve the problem. -Suppose that P(x) represents the percentage of income spent on housing in year x and I(x) represents income in year x. Determine a function H that represents total housing expenditures in year x.

Solve the problem. -A retail store buys 225 VCRs from a distributor at a cost of $205 each plus an overhead charge of $20 per order. The retail markup is 40% on the total price paid. Find the profit on the sale of one VCR.

Find and simplify the difference quotient of f f(x+h) −f(x) h\frac { f ( x + h ) - f ( x ) } { h }hf(x+h) −f(x) ​ , h ≠ 0, for the function. - (x) =17x( x ) = \frac { 1 } { 7 x }(x) =7x1​

Find and simplify the difference quotient of f f(x+h) −f(x) h\frac { f ( x + h ) - f ( x ) } { h }hf(x+h) −f(x) ​ , h ≠ 0, for the function. - f(x) =x2+6x−8f ( x ) = x ^ { 2 } + 6 x - 8f(x) =x2+6x−8

Solve the problem. -Express the gross salary G of a person who earns $40 per hour as a function of the number x of hours worked.

For the given functions f and g, find the requested function and state its domain. - f(x) =7−x;g(x) =x−3f ( x ) = \sqrt { 7 - x } ; g ( x ) = \sqrt { x - 3 }f(x) =7−x​;g(x) =x−3​ Find f⋅gf \cdot gf⋅g .

For the given functions f and g, find the requested function and state its domain. - f(x) =16−x2;g(x) =4−xf ( x ) = 16 - x ^ { 2 } ; g ( x ) = 4 - xf(x) =16−x2;g(x) =4−x Find f+gf + gf+g .

Determine whether the graph is that of a function. If it is, use the graph to find its domain and range, the intercepts, if any, and any symmetry with respect to the x-axis, the y-axis, or the origin. -

Determine whether the graph is that of a function. If it is, use the graph to find its domain and range, the intercepts, if any, and any symmetry with respect to the x-axis, the y-axis, or the origin. -

For the given functions f and g, find the requested function and state its domain. - f(x) =5x3−2;g(x) =5x2+3f ( x ) = 5 x ^ { 3 } - 2 ; g ( x ) = 5 x ^ { 2 } + 3f(x) =5x3−2;g(x) =5x2+3 Find f⋅gf \cdot gf⋅g .

For the given functions f and g, find the requested function and state its domain. - f(x) =5x−89x−2;g(x) =3x9x−2f ( x ) = \frac { 5 x - 8 } { 9 x - 2 } ; g ( x ) = \frac { 3 x } { 9 x - 2 }f(x) =9x−25x−8​;g(x) =9x−23x​ Find f - g.

Solve the problem. -Jacey, a commissioned salesperson, earns $180 base pay plus $47 per item sold. Express Jacey's gross salary G as a function of the number x of items sold.

For the given functions f and g, find the requested function and state its domain. - $f ( x ) = \sqrt { x } ; g ( x ) = 5 x - 8$ Find $\frac { \mathrm { f } } { \mathrm { g } }$ .

For the given functions f and g, find the requested function and state its domain. - $\begin{array} { l } f ( x ) = x + 6 ; g ( x ) = 3 x ^ { 2 } \\ { Find } f + g\end{array}$

Find and simplify the difference quotient of f $\frac { f ( x + h ) - f ( x ) } { h }$ , h ≠ 0, for the function. -f(x) = 4x - 2

For the given functions f and g, find the requested function and state its domain. -f(x) = 5x + 4; g(x) = 5x - 3 $\text { Find } \frac { \mathrm { f } } { \mathrm { g } } \text {. }$

For the given functions f and g, find the requested function and state its domain. - $f ( x ) = \sqrt { x + 13 } ; g ( x ) = \frac { 4 } { x }$ Find f · g.

Find and simplify the difference quotient of f $\frac { f ( x + h ) - f ( x ) } { h }$ , h ≠ 0, for the function. - $( x ) = \frac { 1 } { 7 x }$

Find and simplify the difference quotient of f $\frac { f ( x + h ) - f ( x ) } { h }$ , h ≠ 0, for the function. - $f ( x ) = x ^ { 2 } + 6 x - 8$

For the given functions f and g, find the requested function and state its domain. - $f ( x ) = \sqrt { 7 - x } ; g ( x ) = \sqrt { x - 3 }$ Find $f \cdot g$ .

For the given functions f and g, find the requested function and state its domain. - $f ( x ) = 16 - x ^ { 2 } ; g ( x ) = 4 - x$ Find $f + g$ .

For the given functions f and g, find the requested function and state its domain. - $f ( x ) = 5 x ^ { 3 } - 2 ; g ( x ) = 5 x ^ { 2 } + 3$ Find $f \cdot g$ .

For the given functions f and g, find the requested function and state its domain. - $f ( x ) = \frac { 5 x - 8 } { 9 x - 2 } ; g ( x ) = \frac { 3 x } { 9 x - 2 }$ Find f - g.