Question 1

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

Accepted Answer

A)  $( f \cdot g ) ( x ) = \sqrt { ( 6 - x ) ( x - 2 ) } ; \{ x \mid x \neq 2 , x \neq 6 \}$ 
B)  $( f \cdot g ) ( x ) = \sqrt { ( 6 - x ) ( x - 2 ) } ; \{ x \mid 2 \leq x \leq 6 \}$ 
C)  $( f \cdot g ) ( x ) = \sqrt { ( 6 - x ) ( x - 2 ) } ; \{ x \mid x \geq 0 \}$ 
D)  $( \mathrm { f } \cdot \mathrm { g } ) ( \mathrm { x } ) = \sqrt { - \mathrm { x } ^ { 2 } - 12 } ; \{ \mathrm { x } \mid \mathrm { x } \neq 12 \}$ 
A)  $( f \cdot g ) ( x ) = \sqrt { ( 6 - x ) ( x - 2 ) } ; \{ x \mid x \neq 2 , x \neq 6 \}$ 
B)  $( f \cdot g ) ( x ) = \sqrt { ( 6 - x ) ( x - 2 ) } ; \{ x \mid 2 \leq x \leq 6 \}$ 
C)  $( f \cdot g ) ( x ) = \sqrt { ( 6 - x ) ( x - 2 ) } ; \{ x \mid x \geq 0 \}$ 
D)  $( \mathrm { f } \cdot \mathrm { g } ) ( \mathrm { x } ) = \sqrt { - \mathrm { x } ^ { 2 } - 12 } ; \{ \mathrm { x } \mid \mathrm { x } \neq 12 \}$

Question 2

Find an equation of the secant line containing (1, f(1)) and (2, f(2)).
-$$f ( x ) = \frac { 4 } { x + 3 }$$

Accepted Answer

A)  $y = \frac { 1 } { 5 } x + \frac { 4 } { 5 }$ 
B)  $y = \frac { 4 } { 5 } x + \frac { 1 } { 5 }$ 
C)  $y = - \frac { 1 } { 5 } x + \frac { 6 } { 5 }$ 
D)  $y = \frac { 1 } { 5 } x + \frac { 3 } { 2 }$ 
A)  $y = \frac { 1 } { 5 } x + \frac { 4 } { 5 }$ 
B)  $y = \frac { 4 } { 5 } x + \frac { 1 } { 5 }$ 
C)  $y = - \frac { 1 } { 5 } x + \frac { 6 } { 5 }$ 
D)  $y = \frac { 1 } { 5 } x + \frac { 3 } { 2 }$

Question 3

Write the word or phrase that best completes each statement or answers the question.
-A gas company has the following rate schedule for natural gas usage in single-family residences:

$$\begin{array} { l l } 
\text { Monthly service charge } & \$ 8.80 \
\text { Per therm service charge}\
\text { 1st }  \text { 25 therms } & \text { $\$ 0.6686 /$ therm } \

\text { Over 25  therms } &   \text { $\$ 0.85870 /$ therm }
\end{array}$$

What is the charge for using 25 therms in one month?
What is the charge for using 45 therms in one month?
Construct a function that gives the monthly charge C for x therms of gas.

Accepted Answer

\[\begin{array} { l } 
\$ 25.52 \
\$ 42

Question 4

Determine algebraically whether the function is even, odd, or neither.
-$f ( x ) = \sqrt { x }$

Accepted Answer

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

Question 5

Find the value for the function.
-Find $- f ( x )$ when $f ( x ) = | x | + 9$.

Accepted Answer

A)  $| - x | + 9$ 
B)  $| - x | - 9$ 
C)  $- | x | - 9$ 
D)  $- | x | + 9$ 
A)  $| - x | + 9$ 
B)  $| - x | - 9$ 
C)  $- | x | - 9$ 
D)  $- | x | + 9$

Question 6

Graph the function.
-$f(x)=\left\{\begin{array}{ll}
-x+2 & x<0 \
\sqrt{x}+3 & x \geq 0
\end{array}\right.$

A)

Accepted Answer

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

Question 7

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.
-$$f ( x ) = \frac { 1 } { x } + 2$$
 
 A)

Accepted Answer

B)

C) 
  
D) 
  
B)

C) 
  
D)

Question 8

Graph the function by starting with the graph of the basic function and then using the techniques of shifting,
compressing, stretching, and/or reflecting.
-$$\mathrm { f } ( \mathrm { x } ) = \frac { 1 } { 5 } \mathrm { x } ^ { 2 }$$
 
 A)

Accepted Answer

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

Question 9

For the given functions f and g, find the requested function and state its domain.
-$$f ( x ) = 2 x ^ { 3 } - 1 ; g ( x ) = 5 x ^ { 2 } + 2$$
Find $f \cdot g$.

Accepted Answer

A)  $( \mathrm { f } \cdot \mathrm { g } ) ( \mathrm { x } ) = 10 \mathrm { x } ^ { 5 } + 4 \mathrm { x } ^ { 3 } - 5 \mathrm { x } ^ { 2 } - 2$; all real numbers 
B)  $( \mathrm { f } \cdot \mathrm { g } ) ( \mathrm { x } ) = 10 \mathrm { x } ^ { 6 } + 4 \mathrm { x } ^ { 3 } - 5 \mathrm { x } ^ { 2 } - 2$; all real numbers 
C)  $( \mathrm { f } \cdot \mathrm { g } ) ( \mathrm { x } ) = 2 \mathrm { x } ^ { 3 } + 5 \mathrm { x } ^ { 2 } - 2$; all real numbers 
D)  $( f \cdot g ) ( x ) = 10 x ^ { 5 } + 4 x ^ { 3 } - 5 x ^ { 2 } - 2 ; \{ x \mid x \neq 0 \}$ 
A)  $( \mathrm { f } \cdot \mathrm { g } ) ( \mathrm { x } ) = 10 \mathrm { x } ^ { 5 } + 4 \mathrm { x } ^ { 3 } - 5 \mathrm { x } ^ { 2 } - 2$; all real numbers 
B)  $( \mathrm { f } \cdot \mathrm { g } ) ( \mathrm { x } ) = 10 \mathrm { x } ^ { 6 } + 4 \mathrm { x } ^ { 3 } - 5 \mathrm { x } ^ { 2 } - 2$; all real numbers 
C)  $( \mathrm { f } \cdot \mathrm { g } ) ( \mathrm { x } ) = 2 \mathrm { x } ^ { 3 } + 5 \mathrm { x } ^ { 2 } - 2$; all real numbers 
D)  $( f \cdot g ) ( x ) = 10 x ^ { 5 } + 4 x ^ { 3 } - 5 x ^ { 2 } - 2 ; \{ x \mid x \neq 0 \}$

Question 10

Solve the problem.
-If a rock falls from a height of 70 meters on Earth, the height H (in meters) after x seconds is approximately $$H ( x ) = 70 - 4.9 x ^ { 2 }$$ When does the rock strike the ground? Round to the nearest hundredth, if necessary.

Accepted Answer

A)  14.29 sec 
B)  2.92 sec 
C)  3.78 sec 
D)  1.71 sec 
A)  14.29 sec 
B)  2.92 sec 
C)  3.78 sec 
D)  1.71 sec

Question 11

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

Accepted Answer

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 
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

Question 12

If y varies directly as x, find a linear function which relates them.
-$y = 0.6$ when $x = 1.2$

Accepted Answer

A)  $f ( x ) = 0.6 x$ 
B)  $f ( x ) = 0.5 x$ 
C)  $f ( x ) = x - 0.6$ 
D)  $f ( x ) = 2 x$ 
A)  $f ( x ) = 0.6 x$ 
B)  $f ( x ) = 0.5 x$ 
C)  $f ( x ) = x - 0.6$ 
D)  $f ( x ) = 2 x$

Question 13

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 $$W ( h ) = m \left( \frac { 4000 } { 4000 + h } \right) ^ { 2 }$$ 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 14

Based on the graph, find the range of y = f(x).
-$$f ( x ) = \left\{ \begin{array} { l l } 
4 & \text { if } - 6 \leq x < - 2 \
| x | & \text { if } - 2 \leq x < 5 \
\sqrt [ 3 ] { x } & \text { if } 5 \leq x \leq 12
\end{array} \right.$$
 
 A) $[ 0,5 )$

Accepted Answer

B)  $[ 0,5 ]$ 
C)  $[ 0 , \infty )$ 
D)  $[ 0 , \sqrt [ 3 ] { 12 } ]$ 
B)  $[ 0,5 ]$ 
C)  $[ 0 , \infty )$ 
D)  $[ 0 , \sqrt [ 3 ] { 12 } ]$

Question 15

The graph of a function is given. Determine whether the function is increasing, decreasing, or constant on the given
interval.
-$$( 1,5 )$$

Accepted Answer

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

Question 16

Determine algebraically whether the function is even, odd, or neither.
-$f ( x ) = \frac { 2 x } { | x | }$

Accepted Answer

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

Question 17

Find the average rate of change for the function between the given values.
-$$f ( x ) = 4 x ^ { 2 } ; \text { from } 0 \text { to } \frac { 7 } { 4 }$$

Accepted Answer

A)  $- \frac { 3 } { 10 }$ 
B)  $\frac { 1 } { 3 }$ 
C)  7 
D)  2 
A)  $- \frac { 3 } { 10 }$ 
B)  $\frac { 1 } { 3 }$ 
C)  7 
D)  2

Question 18

Based on the graph, find the range of y = f(x).
-$$f ( x ) = \left\{ \begin{array} { l l } 
- \frac { 1 } { 4 } x & \text { if } x \neq 0 \
- 9 & \text { if } x = 0
\end{array} \right.$$

A) $( - \infty , 0 )$ or $( 0 , \infty )$

Accepted Answer

B)  $( - 10,10 )$ 
C)  $( - \infty , \infty )$ 
D)  $( - \infty , 0 )$ or $\{ 0 \}$ or $( 0 , \infty )$ 
B)  $( - 10,10 )$ 
C)  $( - \infty , \infty )$ 
D)  $( - \infty , 0 )$ or $\{ 0 \}$ or $( 0 , \infty )$

Question 19

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

Accepted Answer

A)  constant function 
B)  absolute value function 
C)  linear function 
D)  reciprocal function 
A)  constant function 
B)  absolute value function 
C)  linear function 
D)  reciprocal function

Question 20

Find the average rate of change for the function between the given values.
-$f ( x ) = x ^ { 3 } + x ^ { 2 } - 8 x - 7 ;$ from 0 to 2

Accepted Answer

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

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

Find an equation of the secant line containing (1, f(1)) and (2, f(2)). - $f ( x ) = \frac { 4 } { x + 3 }$

Determine algebraically whether the function is even, odd, or neither. - $f ( x ) = \sqrt { x }$

Find the value for the function. -Find $- f ( x )$ when $f ( x ) = | x | + 9$ .

For the given functions f and g, find the requested function and state its domain. - $f ( x ) = 2 x ^ { 3 } - 1 ; g ( x ) = 5 x ^ { 2 } + 2$ Find $f \cdot g$ .

Solve the problem. -If a rock falls from a height of 70 meters on Earth, the height H (in meters) after x seconds is approximately $H ( x ) = 70 - 4.9 x ^ { 2 }$ When does the rock strike the ground? Round to the nearest hundredth, if necessary.

If y varies directly as x, find a linear function which relates them. - $y = 0.6$ when $x = 1.2$

The graph of a function is given. Determine whether the function is increasing, decreasing, or constant on the given interval. - $( 1,5 )$

Determine algebraically whether the function is even, odd, or neither. - $f ( x ) = \frac { 2 x } { | x | }$

Find the average rate of change for the function between the given values. - $f ( x ) = 4 x ^ { 2 } ; \text { from } 0 \text { to } \frac { 7 } { 4 }$

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. - $f ( x ) = x ^ { 3 } + x ^ { 2 } - 8 x - 7 ;$ from 0 to 2

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

Review

Filters

Exam 1: Functions and Their Graphs

For the given functions f and g, find the requested function and state its domain. - f(x)=6−x;g(x)=x−2f ( x ) = \sqrt { 6 - x } ; g ( x ) = \sqrt { x - 2 }f(x)=6−x​;g(x)=x−2​ Find f⋅gf \cdot gf⋅g .

Find an equation of the secant line containing (1, f(1)) and (2, f(2)). - f(x)=4x+3f ( x ) = \frac { 4 } { x + 3 }f(x)=x+34​

Determine algebraically whether the function is even, odd, or neither. - f(x)=xf ( x ) = \sqrt { x }f(x)=x​

Find the value for the function. -Find −f(x)- f ( x )−f(x) when f(x)=∣x∣+9f ( x ) = | x | + 9f(x)=∣x∣+9 .

Graph the function. - f(x)={−x+2x<0x+3x≥0f(x)=\left\{\begin{array}{ll}-x+2 & x<0 \\\sqrt{x}+3 & x \geq 0\end{array}\right.f(x)={−x+2x​+3​x<0x≥0​ A) B) C) D)

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)=15x2\mathrm { f } ( \mathrm { x } ) = \frac { 1 } { 5 } \mathrm { x } ^ { 2 }f(x)=51​x2 A) B) C) D)

For the given functions f and g, find the requested function and state its domain. - f(x)=2x3−1;g(x)=5x2+2f ( x ) = 2 x ^ { 3 } - 1 ; g ( x ) = 5 x ^ { 2 } + 2f(x)=2x3−1;g(x)=5x2+2 Find f⋅gf \cdot gf⋅g .

Solve the problem. -If a rock falls from a height of 70 meters on Earth, the height H (in meters) after x seconds is approximately H(x)=70−4.9x2H ( x ) = 70 - 4.9 x ^ { 2 }H(x)=70−4.9x2 When does the rock strike the ground? Round to the nearest hundredth, if necessary.

If y varies directly as x, find a linear function which relates them. - y=0.6y = 0.6y=0.6 when x=1.2x = 1.2x=1.2

The graph of a function is given. Determine whether the function is increasing, decreasing, or constant on the given interval. - (1,5)( 1,5 )(1,5)

Determine algebraically whether the function is even, odd, or neither. - f(x)=2x∣x∣f ( x ) = \frac { 2 x } { | x | }f(x)=∣x∣2x​

Find the average rate of change for the function between the given values. - f(x)=4x2; from 0 to 74f ( x ) = 4 x ^ { 2 } ; \text { from } 0 \text { to } \frac { 7 } { 4 }f(x)=4x2; from 0 to 47​