Question 1

Use the graph of $f ( x ) = | x |$ to write an equation for the function whose graph is shown.

A) $y = | x - 5 | - 1$
B) $y = - | x - 5 | + 1$
C) $y = - | x + 5 | - 1$
D) $y = | x + 5 | + 1$
E) $y = - | x - 5 | - 1$

Accepted Answer

E

Question 2

$\text { A force of } f = 245 \text { newtons stretches a spring } s = 0.25 \text { meter (see figure). }$  How far will a force of 60 newtons stretch the spring? What force is required to stretch the spring 0.2 meter?
A) $ 0.25 \mathrm{~m} ; 196 \mathrm{~N} $
B) $ 0.25 \mathrm{~m} ; 245 \mathrm{~N} $
C) $ 0.06 \mathrm{~m} ; 196 \mathrm{~N} $
D) $ 0.09 \mathrm{~m} ; 285 \mathrm{~N} $
E) $ 0.06 \mathrm{~m} ; 245 \mathrm{~N} $

Accepted Answer

We can use Hooke's Law to solve both parts of the problem. Hooke's Law states that the force required to stretch or compress a spring is directly proportional to the displacement of the spring from its equilibrium position.

For the first part of the problem, we can use the equation:

$f = ks$

where $f$ is the force applied to the spring, $s$ is the displacement of the spring, and $k$ is the spring constant. We can solve for $s$:

$s = \frac{f}{k}$

We are given $f = 245$ N and $s = 0.25$ m. To find $k$, we can rearrange the equation:

$k = \frac{f}{s}$

Substituting in the given values, we get:

$k = \frac{245 	ext{ N}}{0.25 	ext{ m}} = 980 	ext{ N/m}$

Now we can use this value of $k$ to solve for the displacement $s$ when a force of 60 N is applied:

$s = \frac{f}{k} = \frac{60 	ext{ N}}{980 	ext{ N/m}} = 0.0612 	ext{ m} \approx 0.06 	ext{ m}$

For the second part of the problem, we are asked to find the force required to stretch the spring 0.2 m. Again, we can use Hooke's Law:

$f = ks$

We are given $s = 0.2$ m and $k = 980$ N/m. Solving for $f$, we get:

$f = ks = (980 	ext{ N/m})(0.2 	ext{ m}) = 196 	ext{ N}$

Therefore, the answer is Choice C: $0.06$ m, $196$ N.

Question 3

Select the graph of the function $f ( x ) = 3 \| x \|$ 
A)

B)

C)

D)

E)

Accepted Answer

The graph of the function $f ( x ) = 3 \| x \|$ will consist of two lines with slope 3, one passing through the origin and the other passing through the origin and reversed in direction in the negative x-axis. The only graph that matches this description is graph B.

Question 4

Find the inverse function of 
$g ( x ) = x ^ { 7 } - 4$ 
A) $g ^ { - 1 } ( x ) = \sqrt [ 7 ] { x - 4 }$
B) $g ^ { - 1 } ( x ) = ( x + 4 ) ^ { 7 }$
C) $g ^ { - 1 } ( x ) = x ^ { 7 } + 4$
D) $g ^ { - 1 } ( x ) = \sqrt [ 7 ] { x + 4 }$
E) $g ^ { - 1 } ( x ) = ( x - 4 ) ^ { 2 }$

Accepted Answer

To find the inverse function of g(x), we need to solve for x in terms of y. 
So, starting with the given function: 
y = x^7 - 4 
Adding 4 to both sides: 
y + 4 = x^7 
Taking the 7th root of both sides: 
(x + 4)^(1/7) = y^(1/7) 
Switching x and y: 
(y + 4)^(1/7) = x^(1/7) 
Which gives us: 
g^(-1)(x) = (x + 4)^(1/7) 
Therefore, the correct answer is D.

Question 5

Find the inverse function of f informally. $f ( x ) = x ^ { 7 }$
A) $f ^ { - 1 } ( x ) = 7 \sqrt { x }$
B) $f ^ { - 1 } ( x ) = 2 ( \sqrt [ 7 ] { x } )$
C) $f ^ { - 1 } ( x ) = ( \sqrt [ 7 ] { x } ) ^ { 7 }$
D) $f ^ { - 1 } ( x ) = - \sqrt [ 7 ] { x }$
E) $f ^ { - 1 } ( x ) = \sqrt [ 7 ] { x }$

Accepted Answer

To find the inverse function of $f(x) = x^7$, you swap $x$ and $y$ and solve for $y$. This gives $x = y^7$, which means $y = \sqrt[7]{x}$. Therefore, the inverse function is $f^{-1}(x) = \sqrt[7]{x}$.

Question 6

Select the correct graph of the given function. 
$f ( x ) = 2 + \frac { 1 } { x }$
A)

B)

C)

D)

E)

Accepted Answer

The answer of Select the correct graph of the given...

Question 7

$g \text { is related to the parent function. Identify the parent function } f \text {. }$ $g ( x ) = \sqrt { 3 x }$
A) $f ( x ) = \sqrt { 3 x }$
B) $f ( x ) = - \sqrt { 3 x }$
C) $f ( x ) = - \sqrt { x }$
D) $f ( x ) = \sqrt { x }$
E) None of the above

Accepted Answer

The function g(x) is a radical function with a square root, which means it is a transformation of the parent function f(x) = √x. The 3 in front of x indicates a vertical stretch by a factor of 3. Therefore, the parent function is simply f(x) = √x, and the answer is D.

Question 8

Find gof and the domain of composite function. 
$f ( x ) = x ^ { 2 } + 2 , \quad g ( x ) = \sqrt { x }$
A) $( x + 2 ) ^ { 2 }$
Domain of gof: all real numbers $x$
B) $( x - 2 ) ^ { 2 }$
Domain of $g \circ f$ : all real numbers $x$
C) $\sqrt { x ^ { 2 } + 2 }$
Domain of $g \circ f$ : all real numbers $x$
D) $\sqrt { ( x - 2 ) ^ { 2 } }$
Domain of gof: all real numbers $x$
E) $\sqrt { ( x + 2 ) ^ { 2 } }$
Domain of $g \circ f :$ all real numbers $x$

Accepted Answer

To find $g\circ f$, we need to first plug in $f(x)$ into $g(x)$. So we have:
$$(g\circ f)(x) = g(f(x)) = g(x^2+2) = \sqrt{x^2+2}$$
The domain of $g\circ f$ is all real numbers $x$, since the square root function can take any non-negative value as input. Therefore, the correct choice is C.

Question 9

Evaluate the function $g ( y ) = 10 - 4 y \text { at } g ( s + 11 )$ 
A) $34 + 4 s$
B) $34 - 4 s$
C) $- 34 + 4 s$
D) $- 34 - 4 s$
E) $10 - 4 s$

Accepted Answer

The answer of Evaluate the function \(g ( y )...

Question 10

Use the intercept form to find the equation of the line with the given intercepts. The intercept form of the equation of a line with intercepts 
$( a , 0 ) \text { and } ( 0 , b ) \text { is }$ $\frac { x } { a } + \frac { y } { b } = 1 , a \neq 0 , b \neq 0 .$
Point on line: $( - 8,6 )$
$x$-intercept: $( c , 0 )$
$y$-intercept: $( 0 , c ) , \quad c \neq 0$ 
A) $x - y - 2 = 0$
B) $- x + y - 2 = 0$
C) $- x - y - 2 = 0$
D) $x + y - 2 = 0$
E) $x + y - 6 = 0$

Accepted Answer

Given the point $(-8, 6)$ lies on the line and both intercepts are $(c, 0)$ and $(0, c)$, substituting these into the intercept form $\frac{x}{c} + \frac{y}{c} = 1$ gives $x + y = c$. Substituting the point $(-8, 6)$ into this equation gives $-8 + 6 = -2$, so $c = -2$. Thus, the equation becomes $x + y - 2 = 0$.

Question 11

Find the coordinates of a second point on the graph of a function f if the given point is on the graph and the function is even and odd. $( 6 a , 5 c )$ 
A) Even: $( - 6 a , - 5 c )$
Odd: $( - 6 a , 5 c )$
B) Even: $( 6 a , - 5 c )$
Odd: $( - 6 a , - 5 c )$
C) Even: $( - 6 a , - 5 c )$
Odd: $( - 6 a , - 5 c )$
D) Even: $( - 6 a , 5 c )$
Odd: $( 6 a , 5 c )$
E) Even: $( - 6 a , 5 c )$
Odd: $( - 6 a , - 5 c )$

Accepted Answer

For an even function, f(x) = f(-x), so the point (-6a, 5c) is on the graph. For an odd function, f(-x) = -f(x), so the point (-6a, -5c) is on the graph.

Question 12

The suggested retail price of a new hybrid car is p dollars. The dealership advertises a factory rebate of $2000 and a 30% discount. Write a function R in terms of p giving the cost of the hybrid car after receiving the rebate from the
Factory. 
A) $R ( p ) = 2000 - p$
B) $R ( p ) = p - 2000$
C) $R ( p ) = p + 2000$
D) $R ( p ) = p + 600$
E) $R ( p ) = p - 600$

Accepted Answer

The cost of the hybrid car after receiving the rebate from the factory will be the original price minus the rebate, which gives us p - 2000. Then, we take off an additional 30% discount, which is 0.30p. Therefore, the final cost of the hybrid car will be:
R(p) = (p - 2000) - 0.30p
R(p) = 0.70p - 2000
So, the best choice is (B).

Question 13

Find the zeros of the function algebraically. 
$f ( x ) = \sqrt { 7 x + 4 }$
A) $\frac { 4 } { 7 }$
B) $\frac { 7 } { 4 }$
C) $- 4$
D) $- \frac { 4 } { 7 }$
E) $- \frac { 7 } { 4 }$

Accepted Answer

To find the zeros of the function, we set $f(x)$ equal to zero and solve for x: 
$$\sqrt{7x+4}=0$$
This equation has no real solutions because the square root of a non-negative number can never be zero. Therefore, the function has no zeros. The closest answer choice to this is D, which gives a negative value. However, this is not a zero of the function.

Question 14

Approximate the coordinates of the points. 
A) $A : ( 4,5 ) , B : ( - 5 , - 4 ) , C : ( 5,0 ) , D : ( 3 , - 1 )$
B) $A : ( 1,5 ) , B : ( - 5 , - 4 ) , C : ( 5,0 ) , D : ( 3 , - 1 )$
C) $A : ( 2,5 ) , B : ( - 5 , - 4 ) , C : ( 5,0 ) , D ( 3 , - 1 )$
D) $A : ( 3,5 ) , B : ( - 5 , - 4 ) , C : ( 5,0 ) , D : ( 3 , - 1 )$
E) $A : ( - 1,5 ) , B : ( - 5 , - 4 ) , C : ( 5,0 ) , D : ( 3 , - 1 )$

Accepted Answer

The answer of Approximate the coordinates of the points. 
A)...

Question 15

Find the difference quotient and simplify your answer. $$f ( x ) = 5 x - x ^ { 2 } , \quad \frac { f ( 7 + h ) - f ( 7 ) } { h } , \quad h \neq 0$$
A) $- h - 8 , \quad h \neq 0$
B) $- h - 6 , \quad h \neq 0$
C) $- h - 5 , \quad h \neq 0$
D) $- h - 9 , \quad h \neq 0$
E) $- h - 7 , \quad h \neq 0$

Accepted Answer

The answer of Find the difference quotient and simplify your...

Question 16

Use a graphing utility to graph the equation. Use a standard setting. Approximate any intercepts. $$y = | x + 4 |$$ 
A)Intercepts: $( 0 , - 4 ) , ( 0,4 )$

B)Intercepts: $( - 4,0 ) , ( 0 , - 4 )$

C)Intercepts: $( 4,0 ) , ( 0,4 )$

D) Intercepts: $( - 4,0 ) , ( 0,4 )$

E)Intercepts: $( - 4,0 ) , ( 4,0 )$

Accepted Answer

The equation is a absolute value equation, which has a "V" shape. By substituting some trial values of x we can get the first and fourth quadrants' coordinates of the curve. By noticing that the absolute value symbol can be eliminated for positive x values we get the graph of $ y = x + 4 $. When x is negative, by making it positive we get $ y = -x - 4 $ and by multiplying it with -1 we get $ y = x + 4 $. So, the negative x values will also coincide with the positive x values. The graph passes from (-4, 0) and (0, 4) so the answer is D.

Question 17

$\text { Find } ( f / g ) ( x ) \text {. What is the domain of } f / g \text { ? }$ 
$f ( x ) = x ^ { 2 } , \quad g ( x ) = 7 x - 5$
A) $- \frac { x ^ { 2 } } { 7 x - 5 } ;$ all real numbers $x$
B) $\frac { 7 x + 5 } { x ^ { 2 } } ;$ all real numbers $x$ except $x = 0$
C) $\frac { x ^ { 2 } } { 7 x - 5 }$; all real numbers $x$ except $x = \frac { 5 } { 7 }$
D) $\frac { 7 x - 5 } { x ^ { 2 } } ;$ all real numbers $x$ except $x = 0$
E) $\frac { x ^ { 2 } } { 7 x + 5 } ;$ all real numbers $x$ except $x = \frac { 7 } { 5 }$

Accepted Answer

To find $(f/g)(x)$, we simply divide $f(x)$ by $g(x)$.

\begin{align*}
\frac{f(x)}{g(x)} &= \frac{x^2}{7x-5} \
&= \frac{x^2}{7x-5} \cdot \frac{\frac{1}{x^2}}{\frac{1}{x^2}} \quad 	ext{(multiply by }\frac{1}{x^2}	ext{ to get a common denominator)}\
&= \frac{1}{7-\frac{5}{x^2}}
\end{align*}

Thus, $(f/g)(x) = \frac{1}{7-\frac{5}{x^2}}$ with a domain of all real numbers $x$ except for $x=0$ and $x=\pm\sqrt{\frac{5}{7}}$.

The only answer choice that matches this is C.

Question 18

Show that the points form the vertices of the indicated polygon. Right triangle: $( 5,2 ) , ( 2,4 ) , ( - 2 , - 2 )$ 
A) $( \sqrt { 11 } ) ^ { 2 } + ( \sqrt { 52 } ) ^ { 2 } = ( \sqrt { 65 } ) ^ { 2 }$
B) $( \sqrt { 13 } ) ^ { 2 } + ( \sqrt { 52 } ) ^ { 2 } = ( \sqrt { 65 } ) ^ { 2 }$
C) $( \sqrt { 29 } ) ^ { 2 } + ( \sqrt { 52 } ) ^ { 2 } = ( \sqrt { 65 } ) ^ { 2 }$
D) $( \sqrt { 20 } ) ^ { 2 } + ( \sqrt { 52 } ) ^ { 2 } = ( \sqrt { 65 } ) ^ { 2 }$
E) $( \sqrt { 7 } ) ^ { 2 } + ( \sqrt { 52 } ) ^ { 2 } = ( \sqrt { 65 } ) ^ { 2 }$

Accepted Answer

To show that the points form the vertices of a right triangle, we calculate the distances between the points and verify if they satisfy the Pythagorean theorem. The distances between the points $(5,2)$, $(2,4)$, and $(-2,-2)$ are calculated as follows:1. Distance between $(5,2)$ and $(2,4)$: $\sqrt{(5-2)^2 + (2-4)^2} = \sqrt{3^2 + (-2)^2} = \sqrt{9 + 4} = \sqrt{13}$.2. Distance between $(5,2)$ and $(-2,-2)$: $\sqrt{(5-(-2))^2 + (2-(-2))^2} = \sqrt{7^2 + 4^2} = \sqrt{49 + 16} = \sqrt{65}$.3. Distance between $(2,4)$ and $(-2,-2)$: $\sqrt{(2-(-2))^2 + (4-(-2))^2} = \sqrt{4^2 + 6^2} = \sqrt{16 + 36} = \sqrt{52}$.Checking the Pythagorean theorem with these distances, we find that $(\sqrt{13})^2 + (\sqrt{52})^2 = 13 + 52 = 65 = (\sqrt{65})^2$, which matches option B. This confirms that the points form a right triangle.

Question 19

Evaluate the function for the indicated values. $f ( x ) = 4 \llbracket x + 8 \rrbracket + 8$
(i) $f ( 5 )$
(ii) $f ( - 52.7 )$
(iii) $f \left( \frac { 2 } { 3 } \right)$
A) $\begin{array} { l l l } \text { (i) } 60 & \text { (ii) } - 168 & \text { (iii) } 44 \end{array}$
B) $\begin{array} { l l l } \text { (i) } 60 & \text { (ii) } - 168 & \text { (iii) } 40 \end{array}$
C) $\begin{array} { l l l } \text { (i) } 61 & \text { (ii) } - 172 & \text { (iii) } 44 \end{array}$
D) $\begin{array} { l l l } \text { (i) } 61 & \text { (ii) } - 172 & \text { (iii) } 40 \end{array}$
E) $\begin{array} { l l l } \text { (i) } 60 & \text { (ii) } - 172 & \text { (iii) } 40 \end{array}$

Accepted Answer

The function uses the floor function $\llbracket x \rrbracket$, which rounds down to the nearest integer. Calculating each:  (i) $f(5) = 4 \llbracket 5 + 8 \rrbracket + 8 = 4 \times 13 + 8 = 60$  (ii) $f(-52.7) = 4 \llbracket -52.7 + 8 \rrbracket + 8 = 4 \times -45 + 8 = -172$  (iii) $f\left(\frac{2}{3}\right) = 4 \llbracket \frac{2}{3} + 8 \rrbracket + 8 = 4 \times 8 + 8 = 40$

Question 20

Find the x- and y-intercepts of the graph of the equation $y ^ { 2 } = - 9 x + 7$ 
A) $x$-intercept: $\left( - \frac { 7 } { 9 } , 0 \right)$
$y$-intercept: $( 0 , \sqrt { 7 } )$
B) $x$-intercept: $\left( - \frac { 7 } { 9 } , 0 \right)$
$y$-intercept: $( 0 , \pm \sqrt { 7 } )$
C) $x$-intercept: $\left( \frac { 7 } { 9 } , 0 \right)$
$y$-intercept: $( 0 , \sqrt { 7 } )$
D) $x$-intercept: $\left( - \frac { 7 } { 9 } , 0 \right)$
$y$-intercept: $( 0 , - \sqrt { 7 } )$
E) $x$-intercept: $\left( \frac { 7 } { 9 } , 0 \right)$
$y$-intercept: $( 0 , \pm \sqrt { 7 } )$

Accepted Answer

The answer of Find the x- and y-intercepts of the...

Quiz 1: Functions and Their Graphs

Use the graph of $f ( x ) = | x |$ to write an equation for the function whose graph is shown.

Select the graph of the function $f ( x ) = 3 \| x \|$

Find the inverse function of $g ( x ) = x ^ { 7 } - 4$

Find the inverse function of f informally. $f ( x ) = x ^ { 7 }$

Select the correct graph of the given function. $f ( x ) = 2 + \frac { 1 } { x }$

$g \text { is related to the parent function. Identify the parent function } f \text {. }$ $g ( x ) = \sqrt { 3 x }$

Find gof and the domain of composite function. $f ( x ) = x ^ { 2 } + 2 , \quad g ( x ) = \sqrt { x }$

Evaluate the function $g ( y ) = 10 - 4 y \text { at } g ( s + 11 )$

Find the coordinates of a second point on the graph of a function f if the given point is on the graph and the function is even and odd. $( 6 a , 5 c )$

The suggested retail price of a new hybrid car is p dollars. The dealership advertises a factory rebate of $2000 and a 30% discount. Write a function R in terms of p giving the cost of the hybrid car after receiving the rebate from the Factory.

Find the zeros of the function algebraically. $f ( x ) = \sqrt { 7 x + 4 }$

Approximate the coordinates of the points.

Find the difference quotient and simplify your answer. $f ( x ) = 5 x - x ^ { 2 } , \quad \frac { f ( 7 + h ) - f ( 7 ) } { h } , \quad h \neq 0$

Use a graphing utility to graph the equation. Use a standard setting. Approximate any intercepts. $y = | x + 4 |$

$\text { Find } ( f / g ) ( x ) \text {. What is the domain of } f / g \text { ? }$ $f ( x ) = x ^ { 2 } , \quad g ( x ) = 7 x - 5$

Show that the points form the vertices of the indicated polygon. Right triangle: $( 5,2 ) , ( 2,4 ) , ( - 2 , - 2 )$

Evaluate the function for the indicated values. $f ( x ) = 4 \llbracket x + 8 \rrbracket + 8$ (i) $f ( 5 )$ (ii) $f ( - 52.7 )$ (iii) $f \left( \frac { 2 } { 3 } \right)$

Find the x- and y-intercepts of the graph of the equation $y ^ { 2 } = - 9 x + 7$

Quiz 1: Functions and Their Graphs

Use the graph of f(x) =∣x∣f ( x ) = | x |f(x) =∣x∣ to write an equation for the function whose graph is shown.

Select the graph of the function f(x) =3∥x∥f ( x ) = 3 \| x \|f(x) =3∥x∥

Find the inverse function of g(x) =x7−4g ( x ) = x ^ { 7 } - 4g(x) =x7−4

Find the inverse function of f informally. f(x) =x7f ( x ) = x ^ { 7 }f(x) =x7

Select the correct graph of the given function. f(x) =2+1xf ( x ) = 2 + \frac { 1 } { x }f(x) =2+x1​

g is related to the parent function. Identify the parent function f. g \text { is related to the parent function. Identify the parent function } f \text {. }g is related to the parent function. Identify the parent function f. g(x) =3xg ( x ) = \sqrt { 3 x }g(x) =3x​

Find gof and the domain of composite function. f(x) =x2+2,g(x) =xf ( x ) = x ^ { 2 } + 2 , \quad g ( x ) = \sqrt { x }f(x) =x2+2,g(x) =x​

Evaluate the function g(y) =10−4y at g(s+11) g ( y ) = 10 - 4 y \text { at } g ( s + 11 ) g(y) =10−4y at g(s+11)

Find the coordinates of a second point on the graph of a function f if the given point is on the graph and the function is even and odd. (6a,5c) ( 6 a , 5 c ) (6a,5c)

The suggested retail price of a new hybrid car is p dollars. The dealership advertises a factory rebate of $2000 and a 30% discount. Write a function R in terms of p giving the cost of the hybrid car after receiving the rebate from the Factory.

Find the zeros of the function algebraically. f(x) =7x+4f ( x ) = \sqrt { 7 x + 4 }f(x) =7x+4​

Approximate the coordinates of the points.

Find the difference quotient and simplify your answer. f(x) =5x−x2,f(7+h) −f(7) h,h≠0f ( x ) = 5 x - x ^ { 2 } , \quad \frac { f ( 7 + h ) - f ( 7 ) } { h } , \quad h \neq 0f(x) =5x−x2,hf(7+h) −f(7) ​,h=0

Use a graphing utility to graph the equation. Use a standard setting. Approximate any intercepts. y=∣x+4∣y = | x + 4 |y=∣x+4∣

Find (f/g) (x) . What is the domain of f/g ? \text { Find } ( f / g ) ( x ) \text {. What is the domain of } f / g \text { ? } Find (f/g) (x) . What is the domain of f/g ? f(x) =x2,g(x) =7x−5f ( x ) = x ^ { 2 } , \quad g ( x ) = 7 x - 5f(x) =x2,g(x) =7x−5

Show that the points form the vertices of the indicated polygon. Right triangle: (5,2) ,(2,4) ,(−2,−2) ( 5,2 ) , ( 2,4 ) , ( - 2 , - 2 ) (5,2) ,(2,4) ,(−2,−2)

Evaluate the function for the indicated values. f(x) =4⟦x+8⟧+8f ( x ) = 4 \llbracket x + 8 \rrbracket + 8f(x) =4[[x+8]]+8 (i) f(5) f ( 5 ) f(5) (ii) f(−52.7) f ( - 52.7 ) f(−52.7) (iii) f(23) f \left( \frac { 2 } { 3 } \right) f(32​)

Find the x- and y-intercepts of the graph of the equation y2=−9x+7y ^ { 2 } = - 9 x + 7y2=−9x+7

Use the graph of $f ( x ) = | x |$ to write an equation for the function whose graph is shown.

Select the graph of the function $f ( x ) = 3 \| x \|$

Find the inverse function of $g ( x ) = x ^ { 7 } - 4$

Find the inverse function of f informally. $f ( x ) = x ^ { 7 }$

Select the correct graph of the given function. $f ( x ) = 2 + \frac { 1 } { x }$

$g \text { is related to the parent function. Identify the parent function } f \text {. }$ $g ( x ) = \sqrt { 3 x }$

Find gof and the domain of composite function. $f ( x ) = x ^ { 2 } + 2 , \quad g ( x ) = \sqrt { x }$

Evaluate the function $g ( y ) = 10 - 4 y \text { at } g ( s + 11 )$

Find the coordinates of a second point on the graph of a function f if the given point is on the graph and the function is even and odd. $( 6 a , 5 c )$

Find the zeros of the function algebraically. $f ( x ) = \sqrt { 7 x + 4 }$

Find the difference quotient and simplify your answer. $f ( x ) = 5 x - x ^ { 2 } , \quad \frac { f ( 7 + h ) - f ( 7 ) } { h } , \quad h \neq 0$

Use a graphing utility to graph the equation. Use a standard setting. Approximate any intercepts. $y = | x + 4 |$

$\text { Find } ( f / g ) ( x ) \text {. What is the domain of } f / g \text { ? }$ $f ( x ) = x ^ { 2 } , \quad g ( x ) = 7 x - 5$

Show that the points form the vertices of the indicated polygon. Right triangle: $( 5,2 ) , ( 2,4 ) , ( - 2 , - 2 )$

Evaluate the function for the indicated values. $f ( x ) = 4 \llbracket x + 8 \rrbracket + 8$ (i) $f ( 5 )$ (ii) $f ( - 52.7 )$ (iii) $f \left( \frac { 2 } { 3 } \right)$

Find the x- and y-intercepts of the graph of the equation $y ^ { 2 } = - 9 x + 7$