Question 1

Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting.
-$f(x)=-|x|$

Accepted Answer

A) 
 
B) 
 
C) 
 
D)

Question 2

Find the x-intercept(s)and the y-intercept of the function.
-f(x)= -2

Accepted Answer

A) (-2, 0), no y-intercept 
B) no x-intercept, (0, -2) 
C) no x-intercept, no y-intercept 
D) (-2, 0), (0, -2)

Question 3

Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting.
-$$f ( x ) = | x - 3 | + 2$$

Accepted Answer

A) 
 
B) 
 
C) 
 
D)

Question 4

The graph of a function is given. Determine whether the function is increasing, decreasing, or constant on the given interval.
-(- 1, 0)

Accepted Answer

A) constant 
B) decreasing 
C) increasing

Question 5

For the given functions f and g, find the requested function and state its domain. Write the domain in interval notation.
-$f ( x ) = 4 x + 5 ; g ( x ) = 6 x - 1 ; \quad$ Find $\frac { f } { g }$

Accepted Answer

A)  $\left( \frac { \mathrm { f } } { \mathrm { g } } \right) ( \mathrm { x } ) = \frac { 4 \mathrm { x } + 5 } { 6 \mathrm { x } - 1 } ; \left( \infty , \frac { 1 } { 6 } \right) \cup \left( \frac { 1 } { 6 } , \infty \right)$ 
B)  $\left( \frac { f } { g } \right) ( x ) = \frac { 6 x - 1 } { 4 x + 5 } ; \left( \infty , \frac { 1 } { 6 } \right) \cup \left( \frac { 1 } { 6 } , \infty \right)$ 
C)  $\left( \frac { f } { g } \right) ( x ) = \frac { 6 x - 1 } { 4 x + 5 } ; \left( \infty , - \frac { 5 } { 4 } \right) \cup \left( - \frac { 5 } { 4 } , \infty \right)$ 
D)  $\left( \frac { \mathrm { f } } { \mathrm { g } } \right) ( \mathrm { x } ) = \frac { 4 \mathrm { x } + 5 } { 6 \mathrm { x } - 1 } ; \left( \infty , - \frac { 5 } { 4 } \right) \cup \left( - \frac { 5 } { 4 } , \infty \right)$

Question 6

Use the vertical line test to determine whether the graph represents a function.
-

Accepted Answer

A) function 
B) not a function

Question 7

Find the domain of the composite function f g. Write the domain in interval notation.
-$$f ( x ) = 8 x + 56 , g ( x ) = x + 6$$

Accepted Answer

A)  $( - \infty , \infty )$ 
B)  $( - \infty , - 7 ) \cup ( - 7 , - 6 ) ( - 6 , \infty )$ 
C)  $( - \infty , - 13 ) \cup ( - 13 , \infty )$ 
D)  $( - \infty , 13 ) \cup ( 13 , \infty )$

Question 8

Use the horizontal line test to determine whether the function is one-to-one.
-

Accepted Answer

A) Yes 
B) No

Question 9

Graph the function.
-f(x)= -2

Accepted Answer

A) 
 
B) 
 
C) 
 
D)

Question 10

Find the rule that defines each piecewise-defined function.
-

Accepted Answer

A)  $f ( x ) = \left\{ \begin{array} { l l } \frac { 4 } { 3 } x + 4 & \text { if } - 3 \leq x \leq 0 \ \frac { 2 } { 3 } x & \text { if } 0  0 \end{array} \right.$ 
C)  $f ( x ) = \left\{ \begin{array} { l l } \frac { 3 } { 4 } x + 4 & \text { if } - 3 \leq x \leq 0 \ \frac { 3 } { 2 } x & \text { if } x \geq 0 \end{array} \right.$ 
D)  $f ( x ) = \left\{ \begin{array} { l l } \frac { 4 } { 3 } x + 4 & \text { if } - 3 \leq x \leq 0 \ \frac { 2 } { 3 } x & \text { if } x > 0 \end{array} \right.$

Question 11

Use the vertical line test to determine whether the graph represents a function.
-

Accepted Answer

A) function 
B) not a function

Question 12

The graph of a function is given. Determine whether the function is increasing, decreasing, or constant on the given interval.
-Find the values of x, if any, at which f has a relative maximum. What are the relative maxima?

Accepted Answer

A) f has a relative maximum at x = 0; the relative maximum is 1 
B) f has a relative maximum at x = -3 and 3; the relative maximum is 0 
C) f has no relative maximum 
D) f has a relative maximum at x = 3; the relative maximum is 1

Question 13

Use the graph to determine the function's domain and range. Write the domain and range in interval notation.
-

Accepted Answer

A)  domain: $[ 0,4 ]$
range: $( - \infty , \infty )$ 
B)  domain: $( - \infty , \infty )$
range: $[ 0,4 ]$ 
C)  domain: $( - \infty , \infty )$
range: $[ 3,4 ]$ 
D)  domain: $[ 3,4 ]$
range: $( - \infty , \infty )$

Question 14

For the given functions f and g, find the requested composite function.
-$f ( x ) = \sqrt { x + 7 } , g ( x ) = 8 x - 11 ; \quad$ Find the function $f \circ g$.

Accepted Answer

A)  $8 \sqrt { x + 7 } - 11$ 
B)  $2 \sqrt { 2 x - 1 }$ 
C)  $8 \sqrt { x - 4 }$ 
D)  $2 \sqrt { 2 x + 1 }$

Question 15

Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting.
-$f(x)=\sqrt{x-3}-6$

Accepted Answer

A) 
 
B) 
 
C) 
 
D)

Question 16

Decide whether or not the functions are inverses of each other.
-$$f ( x ) = \sqrt { x + 3 } , x \geq - 3 ; g ( x ) = x ^ { 2 } + 3$$

Accepted Answer

A) Yes 
B) No

Question 17

Solve the problem.
-A cellular phone plan had the following schedule of charges: 
 What is the charge for 200 minutes of calls in one month? What is the charge for 250 minutes of calls in one month? Construct a function that relates the monthly charge C for x minutes of calls.

Accepted Answer

The answer of Solve the problem.
-A cellular phone plan had...

Question 18

Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting.
-$$f ( x ) = \frac { 1 } { x + 3 }$$

Accepted Answer

A) 
 
B) 
 
C) 
 
D)

Question 19

The graph of a function f is given. Use the graph to answer the question.
-Find the values of x, if any, at which f has a relative minimum. What are the relative minima?

Accepted Answer

A) f has a relative minimum at x = 0; the relative minimum is 2 
B) f has no relative minimum 
C) f has a relative minimum at x = -2 and 2; the relative minimum is 0 
D) f has a relative minimum at x = -2; the relative minimum is 0

Question 20

Use the accompanying graph of y = f(x) to sketch the graph of the indicated equation.
-$y=2 f(x)$

Accepted Answer

A) 
 
B) 
 
C) 
 
D)

Exam 3: Functions

Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting. - $f(x) =-|x|$

Find the x-intercept(s) and the y-intercept of the function. -f(x) = -2

Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting. - $f ( x ) = | x - 3 | + 2$

The graph of a function is given. Determine whether the function is increasing, decreasing, or constant on the given interval. -(- 1, 0)

For the given functions f and g, find the requested function and state its domain. Write the domain in interval notation. - $f ( x ) = 4 x + 5 ; g ( x ) = 6 x - 1 ; \quad$ Find $\frac { f } { g }$

Use the vertical line test to determine whether the graph represents a function. -

Find the domain of the composite function f g. Write the domain in interval notation. - $f ( x ) = 8 x + 56 , g ( x ) = x + 6$

Use the horizontal line test to determine whether the function is one-to-one. -

Graph the function. -f(x) = -2

Use the vertical line test to determine whether the graph represents a function. -

The graph of a function is given. Determine whether the function is increasing, decreasing, or constant on the given interval. -Find the values of x, if any, at which f has a relative maximum. What are the relative maxima?

For the given functions f and g, find the requested composite function. - $f ( x ) = \sqrt { x + 7 } , g ( x ) = 8 x - 11 ; \quad$ Find the function $f \circ g$ .

Decide whether or not the functions are inverses of each other. - $f ( x ) = \sqrt { x + 3 } , x \geq - 3 ; g ( x ) = x ^ { 2 } + 3$

Solve the problem. -A cellular phone plan had the following schedule of charges: What is the charge for 200 minutes of calls in one month? What is the charge for 250 minutes of calls in one month? Construct a function that relates the monthly charge C for x minutes of calls.

The graph of a function f is given. Use the graph to answer the question. -Find the values of x, if any, at which f has a relative minimum. What are the relative minima?

Use the accompanying graph of y = f(x) to sketch the graph of the indicated equation. - $y=2 f(x)$

Exam 3: Functions

Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting. - f(x) =−∣x∣f(x) =-|x|f(x) =−∣x∣

Find the x-intercept(s) and the y-intercept of the function. -f(x) = -2

Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting. - f(x) =∣x−3∣+2f ( x ) = | x - 3 | + 2f(x) =∣x−3∣+2

The graph of a function is given. Determine whether the function is increasing, decreasing, or constant on the given interval. -(- 1, 0)

For the given functions f and g, find the requested function and state its domain. Write the domain in interval notation. - f(x) =4x+5;g(x) =6x−1;f ( x ) = 4 x + 5 ; g ( x ) = 6 x - 1 ; \quadf(x) =4x+5;g(x) =6x−1; Find fg\frac { f } { g }gf​

Use the vertical line test to determine whether the graph represents a function. -

Find the domain of the composite function f g. Write the domain in interval notation. - f(x) =8x+56,g(x) =x+6f ( x ) = 8 x + 56 , g ( x ) = x + 6f(x) =8x+56,g(x) =x+6

Use the horizontal line test to determine whether the function is one-to-one. -

Graph the function. -f(x) = -2

Find the rule that defines each piecewise-defined function. -

Use the vertical line test to determine whether the graph represents a function. -

The graph of a function is given. Determine whether the function is increasing, decreasing, or constant on the given interval. -Find the values of x, if any, at which f has a relative maximum. What are the relative maxima?

Use the graph to determine the function's domain and range. Write the domain and range in interval notation. -

For the given functions f and g, find the requested composite function. - f(x) =x+7,g(x) =8x−11;f ( x ) = \sqrt { x + 7 } , g ( x ) = 8 x - 11 ; \quadf(x) =x+7​,g(x) =8x−11; Find the function f∘gf \circ gf∘g .

Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting. - f(x) =x−3−6f(x) =\sqrt{x-3}-6f(x) =x−3​−6

Decide whether or not the functions are inverses of each other. - f(x) =x+3,x≥−3;g(x) =x2+3f ( x ) = \sqrt { x + 3 } , x \geq - 3 ; g ( x ) = x ^ { 2 } + 3f(x) =x+3​,x≥−3;g(x) =x2+3

Solve the problem. -A cellular phone plan had the following schedule of charges: What is the charge for 200 minutes of calls in one month? What is the charge for 250 minutes of calls in one month? Construct a function that relates the monthly charge C for x minutes of calls.

Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting. - f(x) =1x+3f ( x ) = \frac { 1 } { x + 3 }f(x) =x+31​

The graph of a function f is given. Use the graph to answer the question. -Find the values of x, if any, at which f has a relative minimum. What are the relative minima?

Use the accompanying graph of y = f(x) to sketch the graph of the indicated equation. - y=2f(x) y=2 f(x) y=2f(x)

Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting. - $f(x) =-|x|$

Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting. - $f ( x ) = | x - 3 | + 2$

For the given functions f and g, find the requested function and state its domain. Write the domain in interval notation. - $f ( x ) = 4 x + 5 ; g ( x ) = 6 x - 1 ; \quad$ Find $\frac { f } { g }$

Find the domain of the composite function f g. Write the domain in interval notation. - $f ( x ) = 8 x + 56 , g ( x ) = x + 6$

For the given functions f and g, find the requested composite function. - $f ( x ) = \sqrt { x + 7 } , g ( x ) = 8 x - 11 ; \quad$ Find the function $f \circ g$ .

Decide whether or not the functions are inverses of each other. - $f ( x ) = \sqrt { x + 3 } , x \geq - 3 ; g ( x ) = x ^ { 2 } + 3$

Use the accompanying graph of y = f(x) to sketch the graph of the indicated equation. - $y=2 f(x)$