Question 1

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

Accepted Answer

A)  $- 15$ 
B)  $( - 25 , - 15 ) , ( 17.5,25 )$ 
C)  $( - 15,17.5 )$ 
D)  $- 15,17.5,25$ 
A)  $- 15$ 
B)  $( - 25 , - 15 ) , ( 17.5,25 )$ 
C)  $( - 15,17.5 )$ 
D)  $- 15,17.5,25$

Question 2

Match the graph to the function listed whose graph most resembles the one given.
-

Accepted Answer

A)  cube root function 
B)  square root function 
C)  square function 
D)  cube function 
A)  cube root function 
B)  square root function 
C)  square function 
D)  cube function

Question 3

Find the average rate of change for the function between the given values.
-$f ( x ) = \sqrt { 2 x - 1 } ;$ from 1 to 5

Accepted Answer

A)  $\frac { 1 } { 2 }$ 
B)  $- 2$ 
C)  $- \frac { 1 } { 6 }$ 
D)  $- 28$ 
A)  $\frac { 1 } { 2 }$ 
B)  $- 2$ 
C)  $- \frac { 1 } { 6 }$ 
D)  $- 28$

Question 4

Find the function.
-Find the function that is finally graphed after the following transformations are applied to the graph of $y = \sqrt { x }$. The graph is shifted down 3 units, reflected about the $x$-axis, and finally shifted left 2 units.

Accepted Answer

A)  $y = - \sqrt { x - 2 } + 3$ 
B)  $y = - \sqrt { x + 2 } - 3$ 
C)  $y = - \sqrt { x + 2 } + 3$ 
D)  $y = \sqrt { - x - 2 } - 3$ 
A)  $y = - \sqrt { x - 2 } + 3$ 
B)  $y = - \sqrt { x + 2 } - 3$ 
C)  $y = - \sqrt { x + 2 } + 3$ 
D)  $y = \sqrt { - x - 2 } - 3$

Question 5

Match the graph to the function listed whose graph most resembles the one given.
-

Accepted Answer

A)  square root function 
B)  cube function 
C)  cube root function 
D)  square function 
A)  square root function 
B)  cube function 
C)  cube root function 
D)  square function

Question 6

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

Accepted Answer

A)  $g ( x ) = \frac { x - 6 } { x - 4 }$ 
B)  $g ( x ) = \frac { x + 6 } { x + 4 }$ 
C)  $g ( x ) = \frac { x - 4 } { x - 6 }$ 
D)  $g ( x ) = \frac { x + 4 } { x + 6 }$ 
A)  $g ( x ) = \frac { x - 6 } { x - 4 }$ 
B)  $g ( x ) = \frac { x + 6 } { x + 4 }$ 
C)  $g ( x ) = \frac { x - 4 } { x - 6 }$ 
D)  $g ( x ) = \frac { x + 4 } { x + 6 }$

Question 7

Find an equation of the secant line containing (1, f(1)) and (2, f(2)).
-$$f ( x ) = \sqrt { x + 24 }$$

Accepted Answer

A)  $y = ( \sqrt { 26 } - 5 ) x - \sqrt { 26 } + 10$ 
B)  $y = ( \sqrt { 26 } - 5 ) x + \sqrt { 26 } - 10$ 
C)  $y = ( - \sqrt { 26 } - 5 ) x - \sqrt { 26 } + 10$ 
D)  $y = ( - \sqrt { 26 } + 5 ) x + \sqrt { 26 } - 10$ 
A)  $y = ( \sqrt { 26 } - 5 ) x - \sqrt { 26 } + 10$ 
B)  $y = ( \sqrt { 26 } - 5 ) x + \sqrt { 26 } - 10$ 
C)  $y = ( - \sqrt { 26 } - 5 ) x - \sqrt { 26 } + 10$ 
D)  $y = ( - \sqrt { 26 } + 5 ) x + \sqrt { 26 } - 10$

Question 8

Suppose the point (2, 4) is on the graph of y = f(x). Find a point on the graph of the given function.
-f(x) + 6

Accepted Answer

A)  (2, -6) 
B)  (8, 4) 
C)  (-4, 4) 
D)  (2, 10) 
A)  (2, -6) 
B)  (8, 4) 
C)  (-4, 4) 
D)  (2, 10)

Question 9

Answer the question about the given function.
-Given the function $f ( x ) = \frac { x ^ { 2 } - 8 } { x + 3 }$, if $x = 2$, what is $f ( x )$ ? What point is on the graph of $f$ ?

Accepted Answer

A)  $- \frac { 4 } { 5 } ; \left( 2 , - \frac { 4 } { 5 } \right)$ 
B)  $\frac { 12 } { 5 } ; \left( 2 , \frac { 12 } { 5 } \right)$ 
C)  $\frac { 12 } { 5 } ; \left( \frac { 12 } { 5 } , 2 \right)$ 
D)  $- \frac { 4 } { 5 } ; \left( - \frac { 4 } { 5 } , 2 \right)$ 
A)  $- \frac { 4 } { 5 } ; \left( 2 , - \frac { 4 } { 5 } \right)$ 
B)  $\frac { 12 } { 5 } ; \left( 2 , \frac { 12 } { 5 } \right)$ 
C)  $\frac { 12 } { 5 } ; \left( \frac { 12 } { 5 } , 2 \right)$ 
D)  $- \frac { 4 } { 5 } ; \left( - \frac { 4 } { 5 } , 2 \right)$

Question 10

Solve the problem.
-If an object weighs $m$ pounds at sea level, then its weight $W$ (in pounds) at a height of $h$ miles above sea level is given approximately by $W ( h ) = m \left( \frac { 4000 } { 4000 + h } \right) ^ { 2 }$. How much will a man who weighs 165 pounds at sea level weigh on the top of a mountain which is 14,494 feet above sea level? Round to the nearest hundredth of a pound, if necessary.

Accepted Answer

A)  165 pounds 
B)  $164.77$ pounds 
C)  $7.72$ pounds 
D)  $165.23$ pounds 
A)  165 pounds 
B)  $164.77$ pounds 
C)  $7.72$ pounds 
D)  $165.23$ pounds

Question 11

The graph of a function is given. Determine whether the function is increasing, decreasing, or constant on the given
interval.
-$(-4,-2)$

Accepted Answer

A)  constant 
B)  decreasing 
C)  increasing 
A)  constant 
B)  decreasing 
C)  increasing

Question 12

For the given functions f and g, find the requested function and state its domain.
-$$f ( x ) = x + 6 ; g ( x ) = 7 x ^ { 2 }$$
Find $f + g$.

Accepted Answer

A)  $( f + g ) ( x ) = 7 x ^ { 2 } + x + 6 ; \{ x \mid x \neq - 6 \}$ 
B)  $( f + g ) ( x ) = 7 x ^ { 2 } + x + 6 ;$ all real numbers 
C)  $( f + g ) ( x ) = 7 x ^ { 2 } - x - 6 ;$ all real numbers 
D)  $( f + g ) ( x ) = - 7 x ^ { 2 } + x + 6$; all real numbers 
A)  $( f + g ) ( x ) = 7 x ^ { 2 } + x + 6 ; \{ x \mid x \neq - 6 \}$ 
B)  $( f + g ) ( x ) = 7 x ^ { 2 } + x + 6 ;$ all real numbers 
C)  $( f + g ) ( x ) = 7 x ^ { 2 } - x - 6 ;$ all real numbers 
D)  $( f + g ) ( x ) = - 7 x ^ { 2 } + x + 6$; all real numbers

Question 13

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

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 14

Match the correct function to the graph.
-

Accepted Answer

A)  $y = | 1 - x |$ 
B)  $y = | x + 2 |$ 
C)  $y = x - 2$ 
D)  $y = | 2 - x |$ 
A)  $y = | 1 - x |$ 
B)  $y = | x + 2 |$ 
C)  $y = x - 2$ 
D)  $y = | 2 - x |$

Question 15

Answer the question about the given function.
-$$\text { Given the function } f ( x ) = \frac { x ^ { 2 } - 6 } { x + 2 } \text {, is the point } ( - 1,7 ) \text { on the graph of } f \text { ? }$$

Accepted Answer

A)  Yes 
B)  No 
A)  Yes 
B)  No

Question 16

The graph of a function is given. Decide whether it is even, odd, or neither.
-

Accepted Answer

A)  even 
B)  odd 
C)  neither 
A)  even 
B)  odd 
C)  neither

Question 17

Use the graph to find the intervals on which it is increasing, decreasing, or constant.
-

Accepted Answer

A)  Increasing on $( - \infty , 0 )$; decreasing on $( 0 , \infty )$ 
B)  Decreasing on $( - \infty , \infty )$ 
C)  Decreasing on $( - \infty , 0 )$; increasing on $( 0 , \infty )$ 
D)  Increasing on $( - \infty , \infty )$ 
A)  Increasing on $( - \infty , 0 )$; decreasing on $( 0 , \infty )$ 
B)  Decreasing on $( - \infty , \infty )$ 
C)  Decreasing on $( - \infty , 0 )$; increasing on $( 0 , \infty )$ 
D)  Increasing on $( - \infty , \infty )$

Question 18

Choose the one alternative that best completes the statement or answers the question.
Graph the function by starting with the graph of the basic function and then using the techniques of shifting,
compressing, stretching, and/or reflecting.
-$f(x)=(x+6)^{3}+5$

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 19

Choose the one alternative that best completes the statement or answers the question.
-The figure shown here shows a rectangle inscribed in an isosceles right triangle whose hypotenuse is 4 units long. Express the area A of the rectangle in terms of x.

Accepted Answer

A)  $A ( x ) = 2 x ( 2 - x )$ 
B)  $A ( x ) = x ( 2 - x )$ 
C)  $\mathrm { A } ( \mathrm { x } ) = 2 \mathrm { x } ^ { 2 }$ 
D)  $A ( x ) = 2 x ( x - 2 )$ 
A)  $A ( x ) = 2 x ( 2 - x )$ 
B)  $A ( x ) = x ( 2 - x )$ 
C)  $\mathrm { A } ( \mathrm { x } ) = 2 \mathrm { x } ^ { 2 }$ 
D)  $A ( x ) = 2 x ( x - 2 )$

Question 20

For the graph of the function y = f(x), find the absolute maximum and the absolute minimum, if it exists.
-

Accepted Answer

A)  Absolute maximum: none; Absolute minimum: none 
B)  Absolute maximum: none; Absolute minimum: $f ( 1 ) = 2$ 
C)  Absolute maximum: $f ( - 1 ) = 6$; Absolute minimum: $f ( 1 ) = 2$ 
D)  Absolute maximum: $f ( 3 ) = 5$; Absolute minimum: $f ( 1 ) = 2$ 
A)  Absolute maximum: none; Absolute minimum: none 
B)  Absolute maximum: none; Absolute minimum: $f ( 1 ) = 2$ 
C)  Absolute maximum: $f ( - 1 ) = 6$; Absolute minimum: $f ( 1 ) = 2$ 
D)  Absolute maximum: $f ( 3 ) = 5$; Absolute minimum: $f ( 1 ) = 2$

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

Match the graph to the function listed whose graph most resembles the one given. -

Find the average rate of change for the function between the given values. - $f ( x ) = \sqrt { 2 x - 1 } ;$ from 1 to 5

Find the function. -Find the function that is finally graphed after the following transformations are applied to the graph of $y = \sqrt { x }$ . The graph is shifted down 3 units, reflected about the $x$ -axis, and finally shifted left 2 units.

Match the graph to the function listed whose graph most resembles the one given. -

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

Find an equation of the secant line containing (1, f(1)) and (2, f(2)). - $f ( x ) = \sqrt { x + 24 }$

Suppose the point (2, 4) is on the graph of y = f(x). Find a point on the graph of the given function. -f(x) + 6

Answer the question about the given function. -Given the function $f ( x ) = \frac { x ^ { 2 } - 8 } { x + 3 }$ , if $x = 2$ , what is $f ( x )$ ? What point is on the graph of $f$ ?

The graph of a function is given. Determine whether the function is increasing, decreasing, or constant on the given interval. - $(-4,-2)$

For the given functions f and g, find the requested function and state its domain. - $f ( x ) = x + 6 ; g ( x ) = 7 x ^ { 2 }$ Find $f + g$ .

Match the correct function to the graph. -

Answer the question about the given function. - $\text { Given the function } f ( x ) = \frac { x ^ { 2 } - 6 } { x + 2 } \text {, is the point } ( - 1,7 ) \text { on the graph of } f \text { ? }$

The graph of a function is given. Decide whether it is even, odd, or neither. -

Use the graph to find the intervals on which it is increasing, decreasing, or constant. -

Choose the one alternative that best completes the statement or answers the question. -The figure shown here shows a rectangle inscribed in an isosceles right triangle whose hypotenuse is 4 units long. Express the area A of the rectangle in terms of x.

For the graph of the function y = f(x), find the absolute maximum and the absolute minimum, if it exists. -

Linear and Quadratic Functions

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometric Functions

Polar Coordinates; Vectors

Analytic Geometry

Systems of Equations and Inequalities

Sequences; Induction; the Binomial Theorem

Counting and Probability

A Preview of Calculus: the Limit, Derivative, and Integral of a Function

Foundations: a Prelude to Functions

Graphing Utilities

Filters

Exam 1: Functions and Their Graphs

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 ?

Match the graph to the function listed whose graph most resembles the one given. -

Find the average rate of change for the function between the given values. - f(x)=2x−1;f ( x ) = \sqrt { 2 x - 1 } ;f(x)=2x−1​; from 1 to 5

Find the function. -Find the function that is finally graphed after the following transformations are applied to the graph of y=xy = \sqrt { x }y=x​ . The graph is shifted down 3 units, reflected about the xxx -axis, and finally shifted left 2 units.

Match the graph to the function listed whose graph most resembles the one given. -

Solve the problem. -Given f(x)=1xf ( x ) = \frac { 1 } { x }f(x)=x1​ and (fg)(x)=x−4x2−6x\left( \frac { f } { g } \right) ( x ) = \frac { x - 4 } { x ^ { 2 } - 6 x }(gf​)(x)=x2−6xx−4​ , find the function ggg .

Find an equation of the secant line containing (1, f(1)) and (2, f(2)). - f(x)=x+24f ( x ) = \sqrt { x + 24 }f(x)=x+24​

Suppose the point (2, 4) is on the graph of y = f(x). Find a point on the graph of the given function. -f(x) + 6

Answer the question about the given function. -Given the function f(x)=x2−8x+3f ( x ) = \frac { x ^ { 2 } - 8 } { x + 3 }f(x)=x+3x2−8​ , if x=2x = 2x=2 , what is f(x)f ( x )f(x) ? What point is on the graph of fff ?

The graph of a function is given. Determine whether the function is increasing, decreasing, or constant on the given interval. - (−4,−2)(-4,-2)(−4,−2)

For the given functions f and g, find the requested function and state its domain. - f(x)=x+6;g(x)=7x2f ( x ) = x + 6 ; g ( x ) = 7 x ^ { 2 }f(x)=x+6;g(x)=7x2 Find f+gf + 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)3f(x)=(-x)^{3}f(x)=(−x)3

Match the correct function to the graph. -

The graph of a function is given. Decide whether it is even, odd, or neither. -

Use the graph to find the intervals on which it is increasing, decreasing, or constant. -

Choose the one alternative that best completes the statement or answers the question. 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+6)3+5f(x)=(x+6)^{3}+5f(x)=(x+6)3+5

Choose the one alternative that best completes the statement or answers the question. -The figure shown here shows a rectangle inscribed in an isosceles right triangle whose hypotenuse is 4 units long. Express the area A of the rectangle in terms of x.

For the graph of the function y = f(x), find the absolute maximum and the absolute minimum, if it exists. -

Linear and Quadratic Functions

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometric Functions

Polar Coordinates; Vectors

Analytic Geometry

Systems of Equations and Inequalities

Sequences; Induction; the Binomial Theorem

Counting and Probability

A Preview of Calculus: the Limit, Derivative, and Integral of a Function

Foundations: a Prelude to Functions

Graphing Utilities

Filters

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

Find the average rate of change for the function between the given values. - $f ( x ) = \sqrt { 2 x - 1 } ;$ from 1 to 5

Find the function. -Find the function that is finally graphed after the following transformations are applied to the graph of $y = \sqrt { x }$ . The graph is shifted down 3 units, reflected about the $x$ -axis, and finally shifted left 2 units.

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

Find an equation of the secant line containing (1, f(1)) and (2, f(2)). - $f ( x ) = \sqrt { x + 24 }$

Answer the question about the given function. -Given the function $f ( x ) = \frac { x ^ { 2 } - 8 } { x + 3 }$ , if $x = 2$ , what is $f ( x )$ ? What point is on the graph of $f$ ?

The graph of a function is given. Determine whether the function is increasing, decreasing, or constant on the given interval. - $(-4,-2)$

For the given functions f and g, find the requested function and state its domain. - $f ( x ) = x + 6 ; g ( x ) = 7 x ^ { 2 }$ Find $f + g$ .