Question 1

Assume that y is directly proportional to x.If x = 28 and y = 21, determine a linear model that relates y and x.

Accepted Answer

A)  $y = \frac { 3 } { 5 } x$ 
B)  $y = \frac { 4 } { 3 } x$ 
C)  $y = \frac { 3 } { 4 } x$ 
D)  $y = \frac { 2 } { 3 } x$ 
E)  $y = \frac { 3 } { 2 } x$ 
A)  $y = \frac { 3 } { 5 } x$ 
B)  $y = \frac { 4 } { 3 } x$ 
C)  $y = \frac { 3 } { 4 } x$ 
D)  $y = \frac { 2 } { 3 } x$ 
E)  $y = \frac { 3 } { 2 } x$

Question 2

Find $g \circ f$ and the domain of the composite function. 
 $f ( x ) = | x | , g ( x ) = x + 4$

Accepted Answer

A)  $| x - 4 |$ Domain of $g \circ f$ : all real numbers x 
B)  $x - | 4 |$ Domain of $g \circ f$ : all real numbers x 
C)  $| x | - 4$ Domain of $g \circ f$ : all real numbers x 
D)  $| x | + 4$ Domain of $g \circ f$ : all real numbers x 
E)  $| x + 4 |$ Domain of $g \circ f$ : all real numbers x 
A)  $| x - 4 |$ Domain of $g \circ f$ : all real numbers x 
B)  $x - | 4 |$ Domain of $g \circ f$ : all real numbers x 
C)  $| x | - 4$ Domain of $g \circ f$ : all real numbers x 
D)  $| x | + 4$ Domain of $g \circ f$ : all real numbers x 
E)  $| x + 4 |$ Domain of $g \circ f$ : all real numbers x

Question 3

Evaluate the indicated function for $f ( x ) = x ^ { 2 } + 3$ and $g ( x ) = x - 6$ . $( f - g ) ( 0 )$

Accepted Answer

A) 48 
B) 39 
C) 9 
D) 0 
E) -39 
A) 48 
B) 39 
C) 9 
D) 0 
E) -39

Question 4

Evaluate the function $f ( x ) = \left\{ \begin{array} { c } 
9 - 2 x , x  2
\end{array} \right.$ at f(7).

Accepted Answer

A) f(7) = 61 
B) f(7) = 58 
C) f(7) = 57 
D) f(7) = 59 
E) f(7) = 60 
A) f(7) = 61 
B) f(7) = 58 
C) f(7) = 57 
D) f(7) = 59 
E) f(7) = 60

Question 5

Find the slope and y-intercept (if possible) of the equation of the line.Select the correct answer for the line.   $3 y + 6 = 0$

Accepted Answer

A)     m = 0y-intercept: (0, -2) 
B)     m = 0There is no y-intercept. 
C)    m = -6y-intercept: (0, 3) 
D)     m = -3y-intercept: (0, 6) 
E)      m is undefined.y-intercept: (0, -2) 
A)     m = 0y-intercept: (0, -2) 
B)     m = 0There is no y-intercept. 
C)    m = -6y-intercept: (0, 3) 
D)     m = -3y-intercept: (0, 6) 
E)      m is undefined.y-intercept: (0, -2)

Question 6

Select the linear function such that it has the indicated function values. 
$f ( - 4 ) = - 2 , f ( 4 ) = - 2$

Accepted Answer

A) f(x) = -x 
B) f(x) = 2 
C) f(x) = -2 
D) f(x) = 4 
E) f(x) = x 
A) f(x) = -x 
B) f(x) = 2 
C) f(x) = -2 
D) f(x) = 4 
E) f(x) = x

Question 7

Find (f + g)(x).   $f ( x ) = x ^ { 2 } + 4 , g ( x ) = \sqrt { 7 - x }$

Accepted Answer

A)  $x ^ { 2 } + 4 - \sqrt { 7 - x }$ 
B)  $x ^ { 2 } + 4 + \sqrt { 7 - x }$ 
C)  $x ^ { 2 } - 4 + \sqrt { 7 + x }$ 
D)  $x ^ { 2 } - 4 - \sqrt { 7 - x }$ 
E)  $x ^ { 2 } - 4 + \sqrt { 7 - x }$ 
A)  $x ^ { 2 } + 4 - \sqrt { 7 - x }$ 
B)  $x ^ { 2 } + 4 + \sqrt { 7 - x }$ 
C)  $x ^ { 2 } - 4 + \sqrt { 7 + x }$ 
D)  $x ^ { 2 } - 4 - \sqrt { 7 - x }$ 
E)  $x ^ { 2 } - 4 + \sqrt { 7 - x }$

Question 8

Evaluate the function at the specified value of the independent variable and simplify. $f ( p ) = \frac { - 8 p } { 9 p + 8 }$ f(y - 5)

Accepted Answer

A)  f(y - 5)= $\frac { - 8 y + 40 } { 9 y - 37 }$ 
B)   f(y - 5)= $\frac { - 8 y - 40 } { 9 y - 37 }$ 
C)   f(y - 5)= $\frac { - 8 p + 40 } { 9 p - 37 }$ 
D)   f(y - 5)= $- \frac { 40 } { 53 }$ 
E) f(y - 5)= $- \frac { 40 } { 37 }$ 
A)  f(y - 5)= $\frac { - 8 y + 40 } { 9 y - 37 }$ 
B)   f(y - 5)= $\frac { - 8 y - 40 } { 9 y - 37 }$ 
C)   f(y - 5)= $\frac { - 8 p + 40 } { 9 p - 37 }$ 
D)   f(y - 5)= $- \frac { 40 } { 53 }$ 
E) f(y - 5)= $- \frac { 40 } { 37 }$

Question 9

Select the correct graph of the given function. 
 $f ( x ) = - x + 5$

Accepted Answer

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

Question 10

Evaluate the function h(x) = [[x + 9]] for x = -4. ​

Accepted Answer

A) ​h(x) = 13 
B) ​h(x) = 5 
C) ​h(x) = 9 
D) ​h(x) = -13 
E) ​h(x) = -5 
A) ​h(x) = 13 
B) ​h(x) = 5 
C) ​h(x) = 9 
D) ​h(x) = -13 
E) ​h(x) = -5

Question 11

Find $f \circ g$ . $f ( x ) = - 2 x - 9 \quad g ( x ) = x + 5$

Accepted Answer

A)  $( f \circ g ) ( x ) = - 2 x - 19$ 
B)  $( f \circ g ) ( x ) = - 3 x - 14$ 
C)  $( f \circ g ) ( x ) = - 2 x ^ { 2 } - 19 x - 45$ 
D)  $( f \circ g ) ( x ) = - 3 x - 4$ 
E)  $( f \circ g ) ( x ) = - 2 x - 4$ 
A)  $( f \circ g ) ( x ) = - 2 x - 19$ 
B)  $( f \circ g ) ( x ) = - 3 x - 14$ 
C)  $( f \circ g ) ( x ) = - 2 x ^ { 2 } - 19 x - 45$ 
D)  $( f \circ g ) ( x ) = - 3 x - 4$ 
E)  $( f \circ g ) ( x ) = - 2 x - 4$

Question 12

Which label corresponds to the coordinates (-3, -5)

Accepted Answer

A) VI 
B) VIII 
C) V 
D) VII 
E) none 
A) VI 
B) VIII 
C) V 
D) VII 
E) none

Question 13

Write an equation for the function that is described by the given characteristic.  
The shape of $f ( x ) = x ^ { 2 }$ , but shifted three units to the right and five units downward.

Accepted Answer

A)  $g ( x ) = ( x - 3 ) ^ { 2 } - 5$ 
B)  $g ( x ) = \left( x ^ { 2 } - 3 \right) - 5$ 
C)  $g ( x ) = ( x + 3 ) ^ { 2 } - 5$ 
D)  $g ( x ) = ( x + 3 ) ^ { 2 } + 5$ 
E)  $g ( x ) = ( x - 3 ) ^ { 2 } + 5$ 
A)  $g ( x ) = ( x - 3 ) ^ { 2 } - 5$ 
B)  $g ( x ) = \left( x ^ { 2 } - 3 \right) - 5$ 
C)  $g ( x ) = ( x + 3 ) ^ { 2 } - 5$ 
D)  $g ( x ) = ( x + 3 ) ^ { 2 } + 5$ 
E)  $g ( x ) = ( x - 3 ) ^ { 2 } + 5$

Question 14

Select the correct graph, showing f and g are inverse functions. 
 $f ( x ) = \frac { x ^ { 3 } } { 7 } , g ( x ) = \sqrt [ 3 ] { 7 x }$

Accepted Answer

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

Question 15

Find the inverse of the one-to-one function.
​
y = 5x + 4
​
f -1(x) = __________

Accepted Answer

Question 16

Identify the parent function and the transformation shown in the graph.Write an equation for the function shown in the graph.

Accepted Answer

A) Horizontal shift of the x-axis of $y = x ^ { 4 } ; y = - x ^ { 4 }$ 
B) Vertical shift of the y-axis of $y = x ^ { 4 } ; y = - x ^ { 4 }$ 
C) Reflection in the x-axis of $y = x ^ { 4 } ; y = - x ^ { 4 }$ 
D) Horizontal shift of the y-axis of $y = x ^ { 4 } ; y = - x ^ { 4 }$ 
E) Vertical shift of the x-axis of $y = x ^ { 4 } ; y = - x ^ { 4 }$ 
A) Horizontal shift of the x-axis of $y = x ^ { 4 } ; y = - x ^ { 4 }$ 
B) Vertical shift of the y-axis of $y = x ^ { 4 } ; y = - x ^ { 4 }$ 
C) Reflection in the x-axis of $y = x ^ { 4 } ; y = - x ^ { 4 }$ 
D) Horizontal shift of the y-axis of $y = x ^ { 4 } ; y = - x ^ { 4 }$ 
E) Vertical shift of the x-axis of $y = x ^ { 4 } ; y = - x ^ { 4 }$

Question 17

Find the coordinates of the point labeled II.

Accepted Answer

A) (-4, -3) 
B) (-4, 3) 
C) (3, 4) 
D) (4, 3) 
E) (-3, -4) 
A) (-4, -3) 
B) (-4, 3) 
C) (3, 4) 
D) (4, 3) 
E) (-3, -4)

Question 18

Evaluate the indicated function for $f ( x ) = x ^ { 2 } + 3$ and $g ( x ) = x - 4$ .   $( f - g ) ( 3 t )$

Accepted Answer

A)  $9 t ^ { 2 } + 3 t + 7$ 
B)  $6 t + 7$ 
C)  $9 t ^ { 2 } + 3 t - 7$ 
D)  $9 t ^ { 2 } - 3 t - 7$ 
E)  $9 t ^ { 2 } - 3 t + 7$ 
A)  $9 t ^ { 2 } + 3 t + 7$ 
B)  $6 t + 7$ 
C)  $9 t ^ { 2 } + 3 t - 7$ 
D)  $9 t ^ { 2 } - 3 t - 7$ 
E)  $9 t ^ { 2 } - 3 t + 7$

Question 19

Plot the points in the Cartesian plane. ​
(-4, 1), (-5, -2), (5, 4), (2, -4)
​

Accepted Answer

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

Question 20

Use the fact that the diameter of the largest particle that can be moved by a stream varies approximately directly as the square of the velocity of the stream.  
A stream with a velocity of $\frac { 1 } { 5 }$ mile per hour can move coarse sand particles about 0.07 inch in diameter.Approximate the velocity required to carry particles 0.2 inch in diameter.(Round your answer to two decimal places.)

Accepted Answer

A) About 0.84 mi/h 
B) About 0.19 mi/h 
C) About -0.16 mi/h 
D) About 0.49 mi/h 
E) About 0.34 mi/h 
A) About 0.84 mi/h 
B) About 0.19 mi/h 
C) About -0.16 mi/h 
D) About 0.49 mi/h 
E) About 0.34 mi/h

Assume that y is directly proportional to x.If x = 28 and y = 21, determine a linear model that relates y and x.

Find $g \circ f$ and the domain of the composite function. $f ( x ) = | x | , g ( x ) = x + 4$

Evaluate the indicated function for $f ( x ) = x ^ { 2 } + 3$ and $g ( x ) = x - 6$ . $( f - g ) ( 0 )$

Evaluate the function $f ( x ) = \left\{ \begin{array} { c } 9 - 2 x , x < - 2 \\0 , \quad - 2 \leq x \leq 2 \\x ^ { 2 } + 8 , x > 2\end{array} \right.$ at f(7).

Find the slope and y-intercept (if possible) of the equation of the line.Select the correct answer for the line. $3 y + 6 = 0$

Select the linear function such that it has the indicated function values. $f ( - 4 ) = - 2 , f ( 4 ) = - 2$

Find (f + g)(x). $f ( x ) = x ^ { 2 } + 4 , g ( x ) = \sqrt { 7 - x }$

Evaluate the function at the specified value of the independent variable and simplify. $f ( p ) = \frac { - 8 p } { 9 p + 8 }$ f(y - 5)

Select the correct graph of the given function. $f ( x ) = - x + 5$

Evaluate the function h(x) = [[x + 9]] for x = -4.

Find $f \circ g$ . $f ( x ) = - 2 x - 9 \quad g ( x ) = x + 5$

Which label corresponds to the coordinates (-3, -5)

Write an equation for the function that is described by the given characteristic. The shape of $f ( x ) = x ^ { 2 }$ , but shifted three units to the right and five units downward.

Select the correct graph, showing f and g are inverse functions. $f ( x ) = \frac { x ^ { 3 } } { 7 } , g ( x ) = \sqrt [ 3 ] { 7 x }$

Find the inverse of the one-to-one function. y = 5x + 4 f ^-1(x) = __________

Identify the parent function and the transformation shown in the graph.Write an equation for the function shown in the graph.

Find the coordinates of the point labeled II.

Evaluate the indicated function for $f ( x ) = x ^ { 2 } + 3$ and $g ( x ) = x - 4$ . $( f - g ) ( 3 t )$

Plot the points in the Cartesian plane. (-4, 1), (-5, -2), (5, 4), (2, -4)

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

Assume that y is directly proportional to x.If x = 28 and y = 21, determine a linear model that relates y and x.

Find g∘fg \circ fg∘f and the domain of the composite function. f(x)=∣x∣,g(x)=x+4f ( x ) = | x | , g ( x ) = x + 4f(x)=∣x∣,g(x)=x+4

Evaluate the indicated function for f(x)=x2+3f ( x ) = x ^ { 2 } + 3f(x)=x2+3 and g(x)=x−6g ( x ) = x - 6g(x)=x−6 . (f−g)(0)( f - g ) ( 0 )(f−g)(0)

Evaluate the function f(x)={9−2x,x<−20,−2≤x≤2x2+8,x>2f ( x ) = \left\{ \begin{array} { c } 9 - 2 x , x < - 2 \\0 , \quad - 2 \leq x \leq 2 \\x ^ { 2 } + 8 , x > 2\end{array} \right.f(x)=⎩⎨⎧​9−2x,x<−20,−2≤x≤2x2+8,x>2​ at f(7).

Find the slope and y-intercept (if possible) of the equation of the line.Select the correct answer for the line. 3y+6=03 y + 6 = 03y+6=0

Select the linear function such that it has the indicated function values. f(−4)=−2,f(4)=−2f ( - 4 ) = - 2 , f ( 4 ) = - 2f(−4)=−2,f(4)=−2

Find (f + g)(x). f(x)=x2+4,g(x)=7−xf ( x ) = x ^ { 2 } + 4 , g ( x ) = \sqrt { 7 - x }f(x)=x2+4,g(x)=7−x​

Evaluate the function at the specified value of the independent variable and simplify. f(p)=−8p9p+8f ( p ) = \frac { - 8 p } { 9 p + 8 }f(p)=9p+8−8p​ f(y - 5)

Select the correct graph of the given function. f(x)=−x+5f ( x ) = - x + 5f(x)=−x+5

Evaluate the function h(x) = [[x + 9]] for x = -4. ​

Find f∘gf \circ gf∘g . f(x)=−2x−9g(x)=x+5f ( x ) = - 2 x - 9 \quad g ( x ) = x + 5f(x)=−2x−9g(x)=x+5

Which label corresponds to the coordinates (-3, -5)

Write an equation for the function that is described by the given characteristic. The shape of f(x)=x2f ( x ) = x ^ { 2 }f(x)=x2 , but shifted three units to the right and five units downward.

Select the correct graph, showing f and g are inverse functions. f(x)=x37,g(x)=7x3f ( x ) = \frac { x ^ { 3 } } { 7 } , g ( x ) = \sqrt [ 3 ] { 7 x }f(x)=7x3​,g(x)=37x​

Find the inverse of the one-to-one function. ​ y = 5x + 4 ​ f -1(x) = __________

Identify the parent function and the transformation shown in the graph.Write an equation for the function shown in the graph.

Find the coordinates of the point labeled II.

Evaluate the indicated function for f(x)=x2+3f ( x ) = x ^ { 2 } + 3f(x)=x2+3 and g(x)=x−4g ( x ) = x - 4g(x)=x−4 . (f−g)(3t)( f - g ) ( 3 t )(f−g)(3t)

Plot the points in the Cartesian plane. ​ (-4, 1), (-5, -2), (5, 4), (2, -4) ​

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

Find $g \circ f$ and the domain of the composite function. $f ( x ) = | x | , g ( x ) = x + 4$

Evaluate the indicated function for $f ( x ) = x ^ { 2 } + 3$ and $g ( x ) = x - 6$ . $( f - g ) ( 0 )$

Evaluate the function $f ( x ) = \left\{ \begin{array} { c } 9 - 2 x , x < - 2 \\0 , \quad - 2 \leq x \leq 2 \\x ^ { 2 } + 8 , x > 2\end{array} \right.$ at f(7).

Find the slope and y-intercept (if possible) of the equation of the line.Select the correct answer for the line. $3 y + 6 = 0$

Select the linear function such that it has the indicated function values. $f ( - 4 ) = - 2 , f ( 4 ) = - 2$

Find (f + g)(x). $f ( x ) = x ^ { 2 } + 4 , g ( x ) = \sqrt { 7 - x }$

Evaluate the function at the specified value of the independent variable and simplify. $f ( p ) = \frac { - 8 p } { 9 p + 8 }$ f(y - 5)

Select the correct graph of the given function. $f ( x ) = - x + 5$

Evaluate the function h(x) = [[x + 9]] for x = -4.

Find $f \circ g$ . $f ( x ) = - 2 x - 9 \quad g ( x ) = x + 5$

Write an equation for the function that is described by the given characteristic. The shape of $f ( x ) = x ^ { 2 }$ , but shifted three units to the right and five units downward.

Select the correct graph, showing f and g are inverse functions. $f ( x ) = \frac { x ^ { 3 } } { 7 } , g ( x ) = \sqrt [ 3 ] { 7 x }$

Find the inverse of the one-to-one function. y = 5x + 4 f ^-1(x) = __________

Evaluate the indicated function for $f ( x ) = x ^ { 2 } + 3$ and $g ( x ) = x - 4$ . $( f - g ) ( 3 t )$

Plot the points in the Cartesian plane. (-4, 1), (-5, -2), (5, 4), (2, -4)