Question 1

Determine whether the function has an inverse function.If it does, find the inverse function.

F(x) = -2

Accepted Answer

A) f-1(x) = 2 
B)  $f ^ { - 1 } ( x ) = - \frac { 1 } { 2 }$ 
C)  $f ^ { - 1 } ( x ) = \frac { 1 } { 2 }$ 
D) f-1(x) = -2 
E) No inverse 
A) f-1(x) = 2 
B)  $f ^ { - 1 } ( x ) = - \frac { 1 } { 2 }$ 
C)  $f ^ { - 1 } ( x ) = \frac { 1 } { 2 }$ 
D) f-1(x) = -2 
E) No inverse

Question 2

Select the graph of the function. 
 $f ( x ) = \left\{ \begin{array} { c c } 
3 + x ^ { 2 } & x < - 2 \
3 + x & - 2 \leq x < 2 \
x ^ { 2 } + 7 & x \geq 2
\end{array} \right.$

Accepted Answer

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

Question 3

After determining whether the variation model below is of the form $y = k x$ or $y = \frac { k } { x }$ , find the value of k. 
$\begin{array} { | c | c | c | c | c | c | } 
\hline x & 154 & 161 & 168 & 175 & 182 \
\hline y & 66 & 69 & 72 & 75 & 78 \
\hline
\end{array}$

Accepted Answer

A)  $k = 7$ 
B)  $k = \frac { 7 } { 3 }$ 
C)  $k = \frac { 1 } { 7 }$ 
D)  $k = \frac { 3 } { 7 }$ 
E)  $k = \frac { 7 } { 66 }$ 
A)  $k = 7$ 
B)  $k = \frac { 7 } { 3 }$ 
C)  $k = \frac { 1 } { 7 }$ 
D)  $k = \frac { 3 } { 7 }$ 
E)  $k = \frac { 7 } { 66 }$

Question 4

The Coca-Cola Company had sales of $19,999 million in 1999 and $29,511 million in 2007.Use the Midpoint Formula to estimate the sales in 2003.Assume that the sales followed a linear pattern. ​

Accepted Answer

A) $24,905 million 
B) $24,855 million 
C) $24,755 million 
D) $24,955 million 
E) $24,805 million 
A) $24,905 million 
B) $24,855 million 
C) $24,755 million 
D) $24,955 million 
E) $24,805 million

Question 5

Evaluate the function at the specified value of the independent variable and simplify. q(p) = -6p - 3
Q(-2.6)
​

Accepted Answer

A) q(-2.6) = 15.6p + 18 
B) q(-2.6) = 18.6 
C) q(-2.6) = 12.6 
D) q(-2.6) = -2.6p - 3 
E) q(-2.6) = -2.6p + 3 
A) q(-2.6) = 15.6p + 18 
B) q(-2.6) = 18.6 
C) q(-2.6) = 12.6 
D) q(-2.6) = -2.6p - 3 
E) q(-2.6) = -2.6p + 3

Question 6

A pharmaceutical salesperson receives a monthly salary of $2600 plus a commission of 2% of sales.Select a linear equation for the sales-person's monthly wage W in terms of monthly sales S.

Accepted Answer

A)  $W = - 0.02 S + 2600$ 
B)  $W = - 0.02 S - 2600$ 
C)  $W = 0.02 S + 2600$ 
D)  $S = 0.02 W - 2600$ 
E)  $S = 0.02 W + 2600$ 
A)  $W = - 0.02 S + 2600$ 
B)  $W = - 0.02 S - 2600$ 
C)  $W = 0.02 S + 2600$ 
D)  $S = 0.02 W - 2600$ 
E)  $S = 0.02 W + 2600$

Question 7

Find the slope of the line passing through the pair of points.  
(10, 12), (12, -12)

Accepted Answer

A)    m = -12 
B)    m = -12 
C)    m = $\frac { 19 } { 14 }$ 
D)    m = $\frac { 19 } { 14 }$ 
E)    m = $\frac { 6 } { 5 }$ 
A)    m = -12 
B)    m = -12 
C)    m = $\frac { 19 } { 14 }$ 
D)    m = $\frac { 19 } { 14 }$ 
E)    m = $\frac { 6 } { 5 }$

Question 8

The length and width of a rectangular garden are 16 meters and 11 meters, respectively.A walkway of width x surrounds the garden.  Write the equation for the perimeter y of the walkway in terms of x.

Accepted Answer

A)  $y = 8 x + 54$ 
B)  $y = 8 x - 54$ 
C)  $y = 8 x + 27$ 
D)  $y = 4 x + 54$ 
E)  $y = 4 x + 27$ 
A)  $y = 8 x + 54$ 
B)  $y = 8 x - 54$ 
C)  $y = 8 x + 27$ 
D)  $y = 4 x + 54$ 
E)  $y = 4 x + 27$

Question 9

Find ( f  - g )(x). 
 $f ( x ) = - \frac { 6 x } { 7 x - 6 } \quad g ( x ) = - \frac { 4 } { x }$

Accepted Answer

A)  $( f - g ) ( x ) = \frac { - 6 x + 34 } { 7 x - 6 }$ 
B)  $( f - g ) ( x ) = \frac { - 6 x ^ { 2 } + 28 x + 24 } { 7 x ^ { 2 } - 6 x }$ 
C)  $( f - g ) ( x ) = \frac { - 3 x + 2 } { 3 x - 3 }$ 
D)  $( f - g ) ( x ) = \frac { - 6 x ^ { 2 } + 28 x - 24 } { 7 x ^ { 2 } - 6 x }$ 
E)  $( f - g ) ( x ) = \frac { - 6 x + 22 } { 7 x - 6 }$ 
A)  $( f - g ) ( x ) = \frac { - 6 x + 34 } { 7 x - 6 }$ 
B)  $( f - g ) ( x ) = \frac { - 6 x ^ { 2 } + 28 x + 24 } { 7 x ^ { 2 } - 6 x }$ 
C)  $( f - g ) ( x ) = \frac { - 3 x + 2 } { 3 x - 3 }$ 
D)  $( f - g ) ( x ) = \frac { - 6 x ^ { 2 } + 28 x - 24 } { 7 x ^ { 2 } - 6 x }$ 
E)  $( f - g ) ( x ) = \frac { - 6 x + 22 } { 7 x - 6 }$

Question 10

An object is dropped from a height of 60 feet. Use the position equation s = -16t2 + v0t + s0 to write a function that represents the situation and select the graph of the function.
​

Accepted Answer

A) s = 16t2 + ​60​​   
B) s = -16t2 - ​60​​   
C) s = 16t2 - ​60​​   
D) s = -16t2 + ​60​​   
E) s = -16t2 + ​60t​​   
A) s = 16t2 + ​60​​   
B) s = -16t2 - ​60​​   
C) s = 16t2 - ​60​​   
D) s = -16t2 + ​60​​   
E) s = -16t2 + ​60t​​

Question 11

Evaluate the function f(x) = 3[[3x - 1]] + 5 for x = 6. ​

Accepted Answer

A) ​f(x) = 51 
B) ​f(x) = -6 
C) ​f(x) = 56 
D) ​f(x) = 6 
E) ​f(x) = 46 
A) ​f(x) = 51 
B) ​f(x) = -6 
C) ​f(x) = 56 
D) ​f(x) = 6 
E) ​f(x) = 46

Question 12

Find the zeros of the function algebraically. 
$f ( x ) = 9 x ^ { 2 } + 21 x - 18$

Accepted Answer

A)   $x = \frac { 2 } { 3 } , - 3$ 
B)   $x = - \frac { 2 } { 3 } , - 3$ 
C)   $x = \frac { 3 } { 2 } , - 3$ 
D)   $x = \frac { 2 } { 3 } , 3$ 
E)   $x = - \frac { 2 } { 3 } , 3$ 
A)   $x = \frac { 2 } { 3 } , - 3$ 
B)   $x = - \frac { 2 } { 3 } , - 3$ 
C)   $x = \frac { 3 } { 2 } , - 3$ 
D)   $x = \frac { 2 } { 3 } , 3$ 
E)   $x = - \frac { 2 } { 3 } , 3$

Question 13

The graph shows the sales (in billions of dollars) for Apple Inc.for the years 2001 through 2007. ​   Find the slope of the line segment connecting the points for the years 2003 and 2004.Round the answer to two decimal places.
​

Accepted Answer

A) -5.07 
B) 2.07 
C) 7.07 
D) 3.07 
E) -2.07 
A) -5.07 
B) 2.07 
C) 7.07 
D) 3.07 
E) -2.07

Question 14

Find (f - g)(x).   $f ( x ) = 2 x - 2 , g ( x ) = 4 - x$

Accepted Answer

A)  $3 x - 6$ 
B)  $2 x + 6$ 
C)  $2 x - 6$ 
D)  $x - 6$ 
E)  $3 x + 6$ 
A)  $3 x - 6$ 
B)  $2 x + 6$ 
C)  $2 x - 6$ 
D)  $x - 6$ 
E)  $3 x + 6$

Question 15

Evaluate q(4) if $q ( x ) = \frac { 1 } { \left( x ^ { 2 } - 7 \right) }$ .

Accepted Answer

A) q(4) = $\frac { 1 } { 13 }$ 
B) q(4) = $\frac { 1 } { 11 }$ 
C) q(4) = $1$ 
D) q(4) = $\frac { 1 } { 12 }$ 
E) q(4) = $\frac { 1 } { 10 }$ 
A) q(4) = $\frac { 1 } { 13 }$ 
B) q(4) = $\frac { 1 } { 11 }$ 
C) q(4) = $1$ 
D) q(4) = $\frac { 1 } { 12 }$ 
E) q(4) = $\frac { 1 } { 10 }$

Question 16

Select the correct graph of the given function. 
 $f ( x ) = - \frac { 8 } { x }$

Accepted Answer

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

Question 17

Use the intercept form to find the equation of the line with the given intercepts.The intercept form of the equation of a line with intercepts (a, 0) and (0, b) is  
  $\frac { x } { a } + \frac { y } { b } = 1 , a \neq 0 , b \neq 0$ 
X-intercept: $\left( - \frac { 1 } { 6 } , 0 \right)$ y-intercept: $\left( 0 , - \frac { 2 } { 7 } \right)$

Accepted Answer

A)  $12 x - 7 y + 2 = 0$ 
B)  $- 12 x + 7 y + 2 = 0$ 
C)  $12 x + 7 y + 2 = 0$ 
D)  $- 7 x - 12 y - 2 = 0$ 
E)  $12 x + 7 y - 2 = 0$ 
A)  $12 x - 7 y + 2 = 0$ 
B)  $- 12 x + 7 y + 2 = 0$ 
C)  $12 x + 7 y + 2 = 0$ 
D)  $- 7 x - 12 y - 2 = 0$ 
E)  $12 x + 7 y - 2 = 0$

Question 18

Select the correct graph, showing f and g are inverse functions. 
 $f ( x ) = 6 - x ^ { 2 } , g ( x ) = \sqrt { 6 - x } , x \leq 6$

Accepted Answer

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

Question 19

Find the domain of the function. 
 $f ( x ) = \frac { \sqrt { x + 4 } } { 4 + x }$

Accepted Answer

A) Non-negative real numbers x B) All real numbers x C) All real numbers x such that x > -4 D) Non-negative real numbers x except x =4 E) All real numbers x such that x < 4 A) Non-negative real numbers x B) All real numbers x C) All real numbers x such that x > -4 D) Non-negative real numbers x except x =4 E) All real numbers x such that x < 4

Question 20

Use the graphs of f and g to evaluate the function.     $$( f \circ g ) ( 3 )$$

Accepted Answer

A) 1 
B) -2 
C) 4 
D) -1 
E) 2 
A) 1 
B) -2 
C) 4 
D) -1 
E) 2

Determine whether the function has an inverse function.If it does, find the inverse function. F(x) = -2

Select the graph of the function. $f ( x ) = \left\{ \begin{array} { c c } 3 + x ^ { 2 } & x < - 2 \\3 + x & - 2 \leq x < 2 \\x ^ { 2 } + 7 & x \geq 2\end{array} \right.$

After determining whether the variation model below is of the form $y = k x$ or $y = \frac { k } { x }$ , find the value of k. x 154 161 168 175 182 y 66 69 72 75 78

The Coca-Cola Company had sales of $19,999 million in 1999 and $29,511 million in 2007.Use the Midpoint Formula to estimate the sales in 2003.Assume that the sales followed a linear pattern.

Evaluate the function at the specified value of the independent variable and simplify. q(p) = -6p - 3 Q(-2.6)

A pharmaceutical salesperson receives a monthly salary of $2600 plus a commission of 2% of sales.Select a linear equation for the sales-person's monthly wage W in terms of monthly sales S.

Find the slope of the line passing through the pair of points. (10, 12), (12, -12)

The length and width of a rectangular garden are 16 meters and 11 meters, respectively.A walkway of width x surrounds the garden. Write the equation for the perimeter y of the walkway in terms of x.

Find ( f - g )(x). $f ( x ) = - \frac { 6 x } { 7 x - 6 } \quad g ( x ) = - \frac { 4 } { x }$

An object is dropped from a height of 60 feet. Use the position equation s = -16t² + v₀t + s₀ to write a function that represents the situation and select the graph of the function.

Evaluate the function f(x) = 3[[3x - 1]] + 5 for x = 6.

Find the zeros of the function algebraically. $f ( x ) = 9 x ^ { 2 } + 21 x - 18$

The graph shows the sales (in billions of dollars) for Apple Inc.for the years 2001 through 2007. Find the slope of the line segment connecting the points for the years 2003 and 2004.Round the answer to two decimal places.

Find (f - g)(x). $f ( x ) = 2 x - 2 , g ( x ) = 4 - x$

Evaluate q(4) if $q ( x ) = \frac { 1 } { \left( x ^ { 2 } - 7 \right) }$ .

Select the correct graph of the given function. $f ( x ) = - \frac { 8 } { x }$

Select the correct graph, showing f and g are inverse functions. $f ( x ) = 6 - x ^ { 2 } , g ( x ) = \sqrt { 6 - x } , x \leq 6$

Find the domain of the function. $f ( x ) = \frac { \sqrt { x + 4 } } { 4 + x }$

Use the graphs of f and g to evaluate the function. $Use the graphs of f and g to evaluate the function. ( f \circ g ) ( 3 )$ $Use the graphs of f and g to evaluate the function. ( f \circ g ) ( 3 )$ $( f \circ g ) ( 3 )$

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometry

Analytic Trigonometry

Additional Topics In Trigonometery

Systems Of Equations and Inequalities

Matrices and Determinants

Sequences Series and Probability

Topics In Analytic Geometry

Analytic Geometry In Three Dimensions

Limits and An Introduction To Calculus

Filters

Exam 1: Functions and Their Graphs

Determine whether the function has an inverse function.If it does, find the inverse function. F(x) = -2

Select the graph of the function. f(x)={3+x2x<−23+x−2≤x<2x2+7x≥2f ( x ) = \left\{ \begin{array} { c c } 3 + x ^ { 2 } & x < - 2 \\3 + x & - 2 \leq x < 2 \\x ^ { 2 } + 7 & x \geq 2\end{array} \right.f(x)=⎩⎨⎧​3+x23+xx2+7​x<−2−2≤x<2x≥2​

After determining whether the variation model below is of the form y=kxy = k xy=kx or y=kxy = \frac { k } { x }y=xk​ , find the value of k. x 154 161 168 175 182 y 66 69 72 75 78

The Coca-Cola Company had sales of $19,999 million in 1999 and $29,511 million in 2007.Use the Midpoint Formula to estimate the sales in 2003.Assume that the sales followed a linear pattern. ​

Evaluate the function at the specified value of the independent variable and simplify. q(p) = -6p - 3 Q(-2.6) ​

A pharmaceutical salesperson receives a monthly salary of $2600 plus a commission of 2% of sales.Select a linear equation for the sales-person's monthly wage W in terms of monthly sales S.

Find the slope of the line passing through the pair of points. (10, 12), (12, -12)

The length and width of a rectangular garden are 16 meters and 11 meters, respectively.A walkway of width x surrounds the garden. Write the equation for the perimeter y of the walkway in terms of x.

Find ( f - g )(x). f(x)=−6x7x−6g(x)=−4xf ( x ) = - \frac { 6 x } { 7 x - 6 } \quad g ( x ) = - \frac { 4 } { x }f(x)=−7x−66x​g(x)=−x4​

An object is dropped from a height of 60 feet. Use the position equation s = -16t2 + v0t + s0 to write a function that represents the situation and select the graph of the function. ​

Evaluate the function f(x) = 3[[3x - 1]] + 5 for x = 6. ​

Find the zeros of the function algebraically. f(x)=9x2+21x−18f ( x ) = 9 x ^ { 2 } + 21 x - 18f(x)=9x2+21x−18

The graph shows the sales (in billions of dollars) for Apple Inc.for the years 2001 through 2007. ​ Find the slope of the line segment connecting the points for the years 2003 and 2004.Round the answer to two decimal places. ​

Find (f - g)(x). f(x)=2x−2,g(x)=4−xf ( x ) = 2 x - 2 , g ( x ) = 4 - xf(x)=2x−2,g(x)=4−x

Evaluate q(4) if q(x)=1(x2−7)q ( x ) = \frac { 1 } { \left( x ^ { 2 } - 7 \right) }q(x)=(x2−7)1​ .

Select the correct graph of the given function. f(x)=−8xf ( x ) = - \frac { 8 } { x }f(x)=−x8​

Select the correct graph, showing f and g are inverse functions. f(x)=6−x2,g(x)=6−x,x≤6f ( x ) = 6 - x ^ { 2 } , g ( x ) = \sqrt { 6 - x } , x \leq 6f(x)=6−x2,g(x)=6−x​,x≤6

Find the domain of the function. f(x)=x+44+xf ( x ) = \frac { \sqrt { x + 4 } } { 4 + x }f(x)=4+xx+4​​

Use the graphs of f and g to evaluate the function. (f∘g)(3)( f \circ g ) ( 3 )(f∘g)(3)

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometry

Analytic Trigonometry

Additional Topics In Trigonometery

Systems Of Equations and Inequalities

Matrices and Determinants

Sequences Series and Probability

Topics In Analytic Geometry

Analytic Geometry In Three Dimensions

Limits and An Introduction To Calculus

Filters

Select the graph of the function. $f ( x ) = \left\{ \begin{array} { c c } 3 + x ^ { 2 } & x < - 2 \\3 + x & - 2 \leq x < 2 \\x ^ { 2 } + 7 & x \geq 2\end{array} \right.$

After determining whether the variation model below is of the form $y = k x$ or $y = \frac { k } { x }$ , find the value of k. x 154 161 168 175 182 y 66 69 72 75 78

The Coca-Cola Company had sales of $19,999 million in 1999 and $29,511 million in 2007.Use the Midpoint Formula to estimate the sales in 2003.Assume that the sales followed a linear pattern.

Evaluate the function at the specified value of the independent variable and simplify. q(p) = -6p - 3 Q(-2.6)

Find ( f - g )(x). $f ( x ) = - \frac { 6 x } { 7 x - 6 } \quad g ( x ) = - \frac { 4 } { x }$

An object is dropped from a height of 60 feet. Use the position equation s = -16t² + v₀t + s₀ to write a function that represents the situation and select the graph of the function.

Evaluate the function f(x) = 3[[3x - 1]] + 5 for x = 6.

Find the zeros of the function algebraically. $f ( x ) = 9 x ^ { 2 } + 21 x - 18$

The graph shows the sales (in billions of dollars) for Apple Inc.for the years 2001 through 2007. Find the slope of the line segment connecting the points for the years 2003 and 2004.Round the answer to two decimal places.

Find (f - g)(x). $f ( x ) = 2 x - 2 , g ( x ) = 4 - x$

Evaluate q(4) if $q ( x ) = \frac { 1 } { \left( x ^ { 2 } - 7 \right) }$ .

Select the correct graph of the given function. $f ( x ) = - \frac { 8 } { x }$

Select the correct graph, showing f and g are inverse functions. $f ( x ) = 6 - x ^ { 2 } , g ( x ) = \sqrt { 6 - x } , x \leq 6$

Find the domain of the function. $f ( x ) = \frac { \sqrt { x + 4 } } { 4 + x }$

Use the graphs of f and g to evaluate the function. $Use the graphs of f and g to evaluate the function. ( f \circ g ) ( 3 )$ $Use the graphs of f and g to evaluate the function. ( f \circ g ) ( 3 )$ $( f \circ g ) ( 3 )$