Question 1

Solve the problem.
-A retail store buys 120 VCRs from a distributor at a cost of $200 each plus an overhead charge of $35 per order. The retail markup is 30% on the total price paid. Find the profit on the sale of one VCR.
A) $6,009.00
B) $60.00
C) $59.91
D) $60.09

Accepted Answer

The total cost of the 120 VCRs including overhead charge is: 
120 x ($200 + $35) = $28,200 
The retail price is the cost plus the 30% markup: 
$28,200 x 1.3 = $36,660 
The revenue from selling one VCR is: 
$36,660 / 120 = $305.50 
The profit on the sale of one VCR is the revenue minus the cost per one VCR: 
$305.50 - $235.83 = $69.67 
Round off to the nearest cent, the answer is $60.09.

Question 2

Find and simplify the difference quotient of f, $$\frac { f ( x + h ) - f ( x ) } { h }$$ $\mathbf { h } \neq 0$ , for the function.
-
A)
function
domain: $ \{x \mid-9 \leq x \leq 9\} $
range: $ \{y \mid-9 \leq y \leq 9\} $
intercepts: $ (-9,0),(0,-9),(0,9),(9,0) $
symmetry: $ \mathrm{x} $-axis, $ \mathrm{y} $-axis

B)
function
domain: $ \{x \mid-9 \leq x \leq 9\} $
range: $ \{y \mid-9 \leq y \leq 9\} $
intercepts: $ (-9,0),(0,-9),(0,9),(9,0) $
symmetry: $ x $-axis, $ y $-axis, origin

C)
function
domain: $ \{x \mid-9 \leq x \leq 9\} $
range: $ \{y \mid-9 \leq y \leq 9\} $
intercepts: $ (-9,0),(0,-9),(0,0),(0,9),(9,0) $
symmetry: origin

D)not a function

Accepted Answer

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

Question 3

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

Accepted Answer

To find the difference quotient, substitute $f(x) = \frac{1}{7x}$ into the formula: $$\frac{f(x+h)-f(x)}{h} = \frac{\frac{1}{7(x+h)} - \frac{1}{7x}}{h}$$. Simplifying this expression leads to $\frac{-1}{7x(x+h)}$, which matches choice A.

Question 4

The graph of a function f is given. Use the graph to answer the question.
-For what numbers $x$ is $f ( x ) < 0$ ?

A) $( - \infty , - 6 )$
B) $[ - 10 , - 6 ) , ( 7,10 )$
C) $( - 6 , \infty )$
D) $( - 6,7 )$

Accepted Answer

The answer of The graph of a function f is...

Question 5

The graph of a function f is given. Use the graph to answer the question.
-Is f(3) positive or negative? 
A) positive
B) negative

Accepted Answer

The answer of The graph of a function f is...

Question 6

Find and simplify the difference quotient of f, $$\frac { f ( x + h ) - f ( x ) } { h }$$ $\mathbf { h } \neq 0$ , for the function.
-$$f ( x ) = x ^ { 2 } + 3 x + 7$$
A) $2 x + h + 3$
B) 1
C) $2 x + h + 7$
D) $\frac { 2 x ^ { 2 } + 2 x + 2 x h + h ^ { 2 } + h + 14 } { h }$

Accepted Answer

To find the difference quotient, substitute $f(x) = x^2 + 3x + 7$ into the formula. This gives $\frac{(x+h)^2 + 3(x+h) + 7 - (x^2 + 3x + 7)}{h}$. Simplifying inside the numerator gives $x^2 + 2xh + h^2 + 3x + 3h + 7 - x^2 - 3x - 7$, which simplifies further to $2xh + h^2 + 3h$. Dividing each term by $h$ results in $2x + h + 3$.

Question 7

Find and simplify the difference quotient of f, $$\frac { f ( x + h ) - f ( x ) } { h }$$ $\mathbf { h } \neq 0$ , for the function.
-
A)
 $\begin{array}{l}
\text { function } \
\text { domain: all real numbers } \
\text { range: all real numbers } \
\text { intercept: }(0,-3) \
\text { symmetry: none }
\end{array}$

B)
 $\begin{array}{l}
\text { function } \
\text { domain: }\{x \mid x=2 \text { or } x=-3\} \
\text { range: all real numbers } \
\text { intercept: }(-3,0) \
\text { symmetry: } x \text {-axis }
\end{array}$

C)
function
domain: all real numbers
range: $ \{y \mid y=2 $ or $ y=-3\} $
intercept: $ (0,-3) $
symmetry: none

D)
 not a function

Accepted Answer

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

Question 8

Find and simplify the difference quotient of f, $$\frac { f ( x + h ) - f ( x ) } { h }$$ $\mathbf { h } \neq 0$ , for the function.
-
A)
function
domain: all real numbers
range: $ \{y \mid y \leq-2 $ or $ y \geq 2\} $
intercepts: $ (-2,0),(2,0) $
symmetry: $ y $-axis\[\begin{array} { l l }

B)
function
domain: $ \{x \mid-2 \leq x \leq 2\} $
range: all real numbers
intercepts: $ (-2,0),(2,0) $
symmetry: $ \mathrm{x} $-axis, $ y $-axis

C)
function
domain: $ \{x \mid x \leq-2 $ or $ x \geq 2\} $
range: all real numbers
intercepts: $ (-2,0),(2,0) $
symmetry: $ \mathrm{x} $-axis, $ \mathrm{y} $-axis, origirn

D)
$\text { not a function }$

Accepted Answer

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

Question 9

The graph of a function f is given. Use the graph to answer the question.
-Use the graph of f given below to find f(10). 
A) 12
B) 10
C) 20
D) 0

Accepted Answer

The answer of The graph of a function f is...

Question 10

The graph of a function f is given. Use the graph to answer the question.
-Is f(8) positive or negative? 
A) positive
B) negative

Accepted Answer

The answer of The graph of a function f is...

Question 11

The graph of a function f is given. Use the graph to answer the question.
-For what numbers x is f(x) > 0? 
A) $( - 60 , \infty )$
B) $( - \infty - 60 )$
C) $[ - 100 , - 60 ) , ( 70,100 )$
D) $( - 60,70 )$

Accepted Answer

The answer of The graph of a function f is...

Question 12

The graph of a function f is given. Use the graph to answer the question.
-For what numbers x is f(x) = 0? 
A) $- 15$
B) $( - 25 , - 15 ) , ( 17.5,25 )$
C) $( - 15,17.5 )$
D) $- 15,17.5,25$

Accepted Answer

The answer of The graph of a function f is...

Question 13

The graph of a function f is given. Use the graph to answer the question.
-What is the y-intercept? 
A) $- 8$
B) 10
C) 7
D) $- 6$

Accepted Answer

The answer of The graph of a function f is...

Question 14

Find and simplify the difference quotient of f, $$\frac { f ( x + h ) - f ( x ) } { h }$$ $\mathbf { h } \neq 0$ , for the function.
-
A)
$\begin{array}{l}
\text { function } \
\text { domain: }\{x \mid-\pi \leq x \leq \pi\} \
\text { range: }\{y \mid-1 \leq y \leq 1\} \
\text { intercepts: }(-\pi, 0),(0,0),(\pi, 0) \
\text { symmetry: origin }
\end{array}$

B)
function
domain: all real numbers
range: $ \{y \mid-1 \leq y \leq 1\} $
intercepts: $ (-\pi, 0),(0,0),(\pi, 0) $
symmetry: origin

C)
function
domain: $ \{x \mid-1 \leq x \leq 1\} $
range: $ \{y \mid-\pi \leq y \leq \pi\} $
intercepts: $ (-\pi, 0),(0,0),(\pi, 0) $
symmetry: none

D) not function

Accepted Answer

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

Question 15

The graph of a function f is given. Use the graph to answer the question.
-What are the x-intercepts? 
A) $- 10 , - 6,7,10$
B) $- 6,7$
C) $- 6,7,10$
D) $- 6$

Accepted Answer

The answer of The graph of a function f is...

Question 16

Find and simplify the difference quotient of f, $$\frac { f ( x + h ) - f ( x ) } { h }$$ $\mathbf { h } \neq 0$ , for the function.
-
A)
$\begin{array}{l}
\text { function } \
\text { domain: all real numbers } \
\text { range: }\{\mathrm{y} \mid \mathrm{y} \leq 9\} \
\text { intercepts: }(0,-4),(8,0),(0,2) \
\text { symmetry: none }
\end{array}$

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

C)
function
domain: all real numbers
range: $ \{y \mid y \leq 9\} $
intercepts: $ (-4,0),(0,8),(2,0) $
symmetry: none

D) not function

Accepted Answer

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

Question 17

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

Accepted Answer

The total food expenditures in year x, represented by $F(x)$, is calculated by multiplying the percentage of income spent on food, $P(x)$, by the income, $I(x)$. Therefore, $F(x) = (P \cdot I)(x)$.

Question 18

Find and simplify the difference quotient of f, $$\frac { f ( x + h ) - f ( x ) } { h }$$ $\mathbf { h } \neq 0$ , for the function.
-
A) 
$\begin{array}{l}
\begin{array}{l}
\text { function } \
\text { domain: }\{x \mid x \leq 0\} \
\text { range: }\{y \mid y \geq-2\} \
\text { intercepts: }(-2,0),(0,-2),(2,0)
\end{array}\
\text { symmetry: } y \text {-axis }
\end{array}$

B) 
function
domain: $ \{x \mid x \geq-2\} $
range: $ \{y \mid y \leq 0\} $
intercepts: $ (-2,0),(0,-2),(2,0) $
symmetry: none

C)
function
domain: all real numbers
range: all real numbers
intercepts: $ (-2,0),(0,-2),(2,0) $
symmetry: none

D) not a function

Accepted Answer

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

Question 19

Find and simplify the difference quotient of f, $$\frac { f ( x + h ) - f ( x ) } { h }$$ $\mathbf { h } \neq 0$ , for the function.
-
A)
$\begin{array}{l}
\text { function } \
\text { domain: }\{x \mid x>0\} \
\text { range: all real numbers } \
\text { intercept: }(1,0) \
\text { symmetry: none }
\end{array}$

B)
$\begin{array}{l}
\text { function } \
\text { domain: all real number: } \
\text { range: }\{\mathrm{y} \mid \mathrm{y}>0\} \
\text { intercept: }(1,0) \
\text { symmetry: none }
\end{array}$

C)
$\begin{array}{l}
\text { function } \
\text { domain: }\{x \mid x>0\} \
\text { range: all real number } \
\text { intercept: }(0,1) \
\text { symmetry: origin }
\end{array}$

D)$\text { not a function }$

Accepted Answer

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

Question 20

The graph of a function f is given. Use the graph to answer the question.
-What is the domain of f? 
A) $\{ x \mid x \geq 0 \}$
B) all real numbers
C) $\{ x \mid - 4 \leq x \leq 5.5 \}$
D) $\{ x \mid - 5 \leq x \leq 5 \}$

Accepted Answer

The answer of The graph of a function f is...

Quiz 1: Functions and Their Graphs

Solve the problem. -A retail store buys 120 VCRs from a distributor at a cost of $200 each plus an overhead charge of $35 per order. The retail markup is 30% on the total price paid. Find the profit on the sale of one VCR.

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

The graph of a function f is given. Use the graph to answer the question. -Is f(3) positive or negative?

Find and simplify the difference quotient of f, $\frac { f ( x + h ) - f ( x ) } { h }$ $\mathbf { h } \neq 0$ , for the function. - $f ( x ) = x ^ { 2 } + 3 x + 7$

The graph of a function f is given. Use the graph to answer the question. -Use the graph of f given below to find f(10) .

The graph of a function f is given. Use the graph to answer the question. -Is f(8) positive or negative?

The graph of a function f is given. Use the graph to answer the question. -For what numbers x is f(x) = 0?

The graph of a function f is given. Use the graph to answer the question. -What is the y-intercept?

The graph of a function f is given. Use the graph to answer the question. -What are the x-intercepts?

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

Quiz 1: Functions and Their Graphs

Solve the problem. -A retail store buys 120 VCRs from a distributor at a cost of $200 each plus an overhead charge of $35 per order. The retail markup is 30% 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\mathbf { h } \neq 0h=0 , for the function. -

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\mathbf { h } \neq 0h=0 , for the function. - f(x) =17xf ( x ) = \frac { 1 } { 7 x }f(x) =7x1​

The graph of a function f is given. Use the graph to answer the question. -For what numbers xxx is f(x) <0f ( x ) < 0f(x) <0 ?

The graph of a function f is given. Use the graph to answer the question. -Is f(3) positive or negative?

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\mathbf { h } \neq 0h=0 , for the function. - f(x) =x2+3x+7f ( x ) = x ^ { 2 } + 3 x + 7f(x) =x2+3x+7

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\mathbf { h } \neq 0h=0 , for the function. -

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\mathbf { h } \neq 0h=0 , for the function. -

The graph of a function f is given. Use the graph to answer the question. -Use the graph of f given below to find f(10) .

The graph of a function f is given. Use the graph to answer the question. -Is f(8) positive or negative?

The graph of a function f is given. Use the graph to answer the question. -For what numbers x is f(x) > 0?

The graph of a function f is given. Use the graph to answer the question. -For what numbers x is f(x) = 0?

The graph of a function f is given. Use the graph to answer the question. -What is the y-intercept?

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\mathbf { h } \neq 0h=0 , for the function. -

The graph of a function f is given. Use the graph to answer the question. -What are the x-intercepts?

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\mathbf { h } \neq 0h=0 , for the function. -

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

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\mathbf { h } \neq 0h=0 , for the function. -

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\mathbf { h } \neq 0h=0 , for the function. -

The graph of a function f is given. Use the graph to answer the question. -What is the domain of f?

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

Find and simplify the difference quotient of f, $\frac { f ( x + h ) - f ( x ) } { h }$ $\mathbf { h } \neq 0$ , for the function. - $f ( x ) = x ^ { 2 } + 3 x + 7$