Question 1

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 2

Answer the question about the given function.
-Given the function $f ( x ) = - 5 x ^ { 2 } + 10 x + 7$, list the $y$-intercept, if there is one, of the graph of $f$.

Accepted Answer

A)  7 
B)  $- 3$ 
C)  12 
D)  $- 8$ 
A)  7 
B)  $- 3$ 
C)  12 
D)  $- 8$

Question 3

The graph of a function f is given. Use the graph to answer the question.
-  Find the numbers, if any, at which f has a local minimum. What are the local maxima? A) f has a local minimum at $x = - 2.5$ and 5 ; the local minimum at $- 2.5$ is $- 3.3$; the local minimum at 5 is $- 2.5$

Accepted Answer

B)  f has a local maximum at $x = - 2.5$ and 5 ; the local maximum at $- 2.5$ is $- 3.3$; the local maximum at 5 is $- 2.5$ 
C)  f has a local minimum at $x = - 3.3$ and $- 2.5$; the local minimum at $- 3.3$ is $- 2.5$; the local minimum at $- 2.5$ is 5 
D)  f has a local maximum at $x = - 3.3$ and $- 2.5$; the local maximum at $- 3.3$ is $- 2.5$; the local maximum at $- 2.5$ is 5 
B)  f has a local maximum at $x = - 2.5$ and 5 ; the local maximum at $- 2.5$ is $- 3.3$; the local maximum at 5 is $- 2.5$ 
C)  f has a local minimum at $x = - 3.3$ and $- 2.5$; the local minimum at $- 3.3$ is $- 2.5$; the local minimum at $- 2.5$ is 5 
D)  f has a local maximum at $x = - 3.3$ and $- 2.5$; the local maximum at $- 3.3$ is $- 2.5$; the local maximum at $- 2.5$ is 5

Question 4

Solve the problem.
-Two boats leave a dock at the same time. One boat is headed directly east at a constant speed of 35 knots
(nautical miles per hour), and the other is headed directly south at a constant speed of 22 knots. Express the
distance d between the boats as a function of the time t.

Accepted Answer

The answer of Solve the problem.
-Two boats leave a dock...

Question 5

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

Accepted Answer

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 
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

Question 6

Find the value for the function.
-$\text { Find } f(-2) \text { when } f(x)=\frac{x^{2}-7}{x-1}$

Accepted Answer

A)  9 
B)  $-\frac{4}{3}$ 
C)  $-\frac{11}{3}$ 
D)  1 
A)  9 
B)  $-\frac{4}{3}$ 
C)  $-\frac{11}{3}$ 
D)  1

Question 7

Determine whether the equation defines y as a function of x.
-$x^{2}+2 y^{2}=1$

Accepted Answer

A)  function 
B)  not a function 
A)  function 
B)  not a function

Question 8

Find the domain of the function.
-$$f ( x ) = - 9 x - 2$$

Accepted Answer

A)  $\{ x \mid x > 0 \}$ 
B)  $\{ x \mid x \neq 0 \}$ 
C)  $\{ x \mid x \geq 2 \}$ 
D)  all real numbers 
A)  $\{ x \mid x > 0 \}$ 
B)  $\{ x \mid x \neq 0 \}$ 
C)  $\{ x \mid x \geq 2 \}$ 
D)  all real numbers

Question 9

Locate any intercepts of the function.
-$$f ( x ) = \left\{ \begin{array} { l l } 
- 5 x + 7 & \text { if } x < 1 \
7 x - 5 & \text { if } x \geq 1
\end{array} \right.$$

Accepted Answer

A)  $( 0 , - 5 ) , \left( \frac { 7 } { 5 } , 0 \right) , \left( \frac { 5 } { 7 } , 0 \right)$
В) $( 0,7 ) , \left( \frac { 7 } { 5 } , 0 \right) , \left( \frac { 5 } { 7 } , 0 \right)$ 
C)  $( 0 , - 5 )$ 
D)  $( 0,7 )$ 
A)  $( 0 , - 5 ) , \left( \frac { 7 } { 5 } , 0 \right) , \left( \frac { 5 } { 7 } , 0 \right)$
В) $( 0,7 ) , \left( \frac { 7 } { 5 } , 0 \right) , \left( \frac { 5 } { 7 } , 0 \right)$ 
C)  $( 0 , - 5 )$ 
D)  $( 0,7 )$

Question 10

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 11

Solve the problem.
-A rectangular sign is being designed so that the length of its base, in feet, is 10 feet less than 4 times the height, h. Express the area of the sign as a function of h. A) $A ( h ) = - 10 h + 4 h ^ { 2 }$

Accepted Answer

B)  $A ( h ) = - 10 h + h ^ { 2 }$ 
C)  $A ( h ) = 10 h - 2 h ^ { 2 }$ 
D)  $A ( h ) = - 10 h ^ { 2 } + 2 h$ 
B)  $A ( h ) = - 10 h + h ^ { 2 }$ 
C)  $A ( h ) = 10 h - 2 h ^ { 2 }$ 
D)  $A ( h ) = - 10 h ^ { 2 } + 2 h$

Question 12

Determine algebraically whether the function is even, odd, or neither.
-$f ( x ) = \frac { 1 } { x ^ { 2 } }$

Accepted Answer

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

Question 13

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

Accepted Answer

A)  reciprocal function 
B)  square function 
C)  cube function 
D)  absolute value function 
A)  reciprocal function 
B)  square function 
C)  cube function 
D)  absolute value function

Question 14

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 15

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 16

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 17

Find the value for the function.
-$\text { Find } f(0) \text { when } f(x)=\sqrt{x^{2}+2 x}$

Accepted Answer

A)  $\sqrt{6}$ 
B)  0 
C)  2 
D)  $\sqrt{2}$ 
A)  $\sqrt{6}$ 
B)  0 
C)  2 
D)  $\sqrt{2}$

Question 18

For the given functions f and g, find the requested function and state its domain.
-$$f ( x ) = 9 x - 5 ; g ( x ) = 4 x - 8$$
Find $f - g$.

Accepted Answer

A)  $( f - g ) ( x ) = 13 x - 13 ; \{ x \mid x \neq 1 \}$ 
B)  $( f - g ) ( x ) = 5 x - 13 ; \left\{ x \mid x \neq \frac { 13 } { 5 } \right\}$ 
C)  $( \mathrm { f } - \mathrm { g } ) ( \mathrm { x } ) = 5 \mathrm { x } + 3$; all real numbers 
D)  $( f - g ) ( x ) = - 5 x - 3$; all real numbers 
A)  $( f - g ) ( x ) = 13 x - 13 ; \{ x \mid x \neq 1 \}$ 
B)  $( f - g ) ( x ) = 5 x - 13 ; \left\{ x \mid x \neq \frac { 13 } { 5 } \right\}$ 
C)  $( \mathrm { f } - \mathrm { g } ) ( \mathrm { x } ) = 5 \mathrm { x } + 3$; all real numbers 
D)  $( f - g ) ( x ) = - 5 x - 3$; all real numbers

Question 19

Match the function with the graph that best describes the situation.
-The concentration C (arbitrary units) of a certain drug in a patient's bloodstream can be modeled using $$C ( t ) = \frac { t } { ( 0.423 t + 2.366 ) ^ { 2 } }$$ where t is the number of hours since a 500 milligram oral dose was administered. Using the TABLE feature of a graphing utility, find the time at which the concentration of the drug is greatest. Round
To the nearest tenth of an hour.

Accepted Answer

A)  5.6 hours 
B)  6.4 hours 
C)  7.1 hours 
D)  7.9 hours 
A)  5.6 hours 
B)  6.4 hours 
C)  7.1 hours 
D)  7.9 hours

Question 20

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

Accepted Answer

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

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

Answer the question about the given function. -Given the function $f ( x ) = - 5 x ^ { 2 } + 10 x + 7$ , list the $y$ -intercept, if there is one, of the graph of $f$ .

Solve the problem. -Two boats leave a dock at the same time. One boat is headed directly east at a constant speed of 35 knots (nautical miles per hour), and the other is headed directly south at a constant speed of 22 knots. Express the distance d between the boats as a function of the time t.

Find the value for the function. - $\text { Find } f(-2) \text { when } f(x)=\frac{x^{2}-7}{x-1}$

Determine whether the equation defines y as a function of x. - $x^{2}+2 y^{2}=1$

Find the domain of the function. - $f ( x ) = - 9 x - 2$

Locate any intercepts of the function. - $f ( x ) = \left\{ \begin{array} { l l } - 5 x + 7 & \text { if } x < 1 \\7 x - 5 & \text { if } x \geq 1\end{array} \right.$

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

Determine algebraically whether the function is even, odd, or neither. - $f ( x ) = \frac { 1 } { x ^ { 2 } }$

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

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

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

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 $f + g$ .

Find the value for the function. - $\text { Find } f(0) \text { when } f(x)=\sqrt{x^{2}+2 x}$

For the given functions f and g, find the requested function and state its domain. - $f ( x ) = 9 x - 5 ; g ( x ) = 4 x - 8$ Find $f - g$ .

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

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

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

Answer the question about the given function. -Given the function f(x)=−5x2+10x+7f ( x ) = - 5 x ^ { 2 } + 10 x + 7f(x)=−5x2+10x+7 , list the yyy -intercept, if there is one, of the graph of fff .

Solve the problem. -Two boats leave a dock at the same time. One boat is headed directly east at a constant speed of 35 knots (nautical miles per hour), and the other is headed directly south at a constant speed of 22 knots. Express the distance d between the boats as a function of the time t.

Find the value for the function. - Find f(−2) when f(x)=x2−7x−1\text { Find } f(-2) \text { when } f(x)=\frac{x^{2}-7}{x-1} Find f(−2) when f(x)=x−1x2−7​

Determine whether the equation defines y as a function of x. - x2+2y2=1x^{2}+2 y^{2}=1x2+2y2=1

Find the domain of the function. - f(x)=−9x−2f ( x ) = - 9 x - 2f(x)=−9x−2

Locate any intercepts of the function. - f(x)={−5x+7 if x<17x−5 if x≥1f ( x ) = \left\{ \begin{array} { l l } - 5 x + 7 & \text { if } x < 1 \\7 x - 5 & \text { if } x \geq 1\end{array} \right.f(x)={−5x+77x−5​ if x<1 if x≥1​

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

Determine algebraically whether the function is even, odd, or neither. - f(x)=1x2f ( x ) = \frac { 1 } { x ^ { 2 } }f(x)=x21​

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

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

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

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 .

Find the value for the function. - Find f(0) when f(x)=x2+2x\text { Find } f(0) \text { when } f(x)=\sqrt{x^{2}+2 x} Find f(0) when f(x)=x2+2x​

For the given functions f and g, find the requested function and state its domain. - f(x)=9x−5;g(x)=4x−8f ( x ) = 9 x - 5 ; g ( x ) = 4 x - 8f(x)=9x−5;g(x)=4x−8 Find f−gf - gf−g .

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

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

Answer the question about the given function. -Given the function $f ( x ) = - 5 x ^ { 2 } + 10 x + 7$ , list the $y$ -intercept, if there is one, of the graph of $f$ .

Find the value for the function. - $\text { Find } f(-2) \text { when } f(x)=\frac{x^{2}-7}{x-1}$

Determine whether the equation defines y as a function of x. - $x^{2}+2 y^{2}=1$

Find the domain of the function. - $f ( x ) = - 9 x - 2$

Locate any intercepts of the function. - $f ( x ) = \left\{ \begin{array} { l l } - 5 x + 7 & \text { if } x < 1 \\7 x - 5 & \text { if } x \geq 1\end{array} \right.$

Determine algebraically whether the function is even, odd, or neither. - $f ( x ) = \frac { 1 } { x ^ { 2 } }$

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 $f + g$ .

Find the value for the function. - $\text { Find } f(0) \text { when } f(x)=\sqrt{x^{2}+2 x}$

For the given functions f and g, find the requested function and state its domain. - $f ( x ) = 9 x - 5 ; g ( x ) = 4 x - 8$ Find $f - g$ .