Question 1

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 2

Solve the problem.
-The gravitational attraction A between two masses varies inversely as the square of the distance between them. The force of attraction is 9 lb when the masses are 2 ft apart, what is the attraction when the masses are 6 ft
Apart?

Accepted Answer

A)  2 lb 
B)  3 lb 
C)  4 lb 
D)  1 lb 
A)  2 lb 
B)  3 lb 
C)  4 lb 
D)  1 lb

Question 3

Suppose the point (2, 4) is on the graph of y = f(x). Find a point on the graph of the given function.
-The reflection of the graph of y = f(x) across the y-axis

Accepted Answer

A)  (-2, -4) 
B)  (2, -4) 
C)  (-2, 4) 
D)  (2, 4) 
A)  (-2, -4) 
B)  (2, -4) 
C)  (-2, 4) 
D)  (2, 4)

Question 4

Answer the question about the given function.
-Given the function $f ( x ) = 3 x ^ { 2 } - 6 x + 7$, what is the domain of $f$ ?

Accepted Answer

A)  all real numbers 
B)  $\{ x \mid x \geq 1 \}$ 
C)  $\{ x \mid x \leq 1 \}$ 
D)  $\{ x \mid x \geq - 1 \}$ 
A)  all real numbers 
B)  $\{ x \mid x \geq 1 \}$ 
C)  $\{ x \mid x \leq 1 \}$ 
D)  $\{ x \mid x \geq - 1 \}$

Question 5

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

Accepted Answer

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

Question 6

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 7

Find the domain of the function.
-$$g ( x ) = \frac { 2 x } { x ^ { 2 } - 81 }$$

Accepted Answer

A)  all real numbers 
B)  $\{ x \mid x \neq 0 \}$ 
C)  $\{ x \mid x > 81 \}$ 
D)  $\{ x \mid x \neq - 9,9 \}$ 
A)  all real numbers 
B)  $\{ x \mid x \neq 0 \}$ 
C)  $\{ x \mid x > 81 \}$ 
D)  $\{ x \mid x \neq - 9,9 \}$

Question 8

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 9

Graph the function by starting with the graph of the basic function and then using the techniques of shifting,
compressing, stretching, and/or reflecting.
-$$f ( x ) = \frac { 1 } { 7 } x ^ { 3 }$$
 
 A)

Accepted Answer

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

Question 10

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: $f ( 1 ) = 2$ 
B)  Absolute maximum: $f ( 4 ) = 7$; Absolute minimum: $f ( 1 ) = 2$ 
C)  Absolute maximum: $f ( 4 ) = 7$; Absolute minimum: none 
D)  Absolute maximum: none; Absolute minimum: none 
A)  Absolute maximum: none; Absolute minimum: $f ( 1 ) = 2$ 
B)  Absolute maximum: $f ( 4 ) = 7$; Absolute minimum: $f ( 1 ) = 2$ 
C)  Absolute maximum: $f ( 4 ) = 7$; Absolute minimum: none 
D)  Absolute maximum: none; Absolute minimum: none

Question 11

Determine whether the relation represents a function. If it is a function, state the domain and range.
-$\{(-1,-3),(-2,-2),(-2,0),(2,2),(14,4)\}$

Accepted Answer

A)  function
domain: $ \{-3,-2,0,2,4\} $
range: $ \{-1,2,-2,14\} $ 
B)  function
domain: $ \{-1,2,-2,14\} $
range: $ \{-3,-2,0,2,4\} $ 
C)  $\text { not a function }$ 
A)  function
domain: $ \{-3,-2,0,2,4\} $
range: $ \{-1,2,-2,14\} $ 
B)  function
domain: $ \{-1,2,-2,14\} $
range: $ \{-3,-2,0,2,4\} $ 
C)  $\text { not a function }$

Question 12

Find the value for the function.
-Find $f ( x + 1 )$ when $f ( x ) = \frac { x ^ { 2 } - 7 } { x + 4 }$

Accepted Answer

A)  $\frac { x ^ { 2 } + 2 x - 6 } { x - 3 }$ 
B)  $\frac { x ^ { 2 } + 2 x + 8 } { x + 5 }$ 
C)  $\frac { x ^ { 2 } - 6 } { x + 5 }$ 
D)  $\frac { x ^ { 2 } + 2 x - 6 } { x + 5 }$ 
A)  $\frac { x ^ { 2 } + 2 x - 6 } { x - 3 }$ 
B)  $\frac { x ^ { 2 } + 2 x + 8 } { x + 5 }$ 
C)  $\frac { x ^ { 2 } - 6 } { x + 5 }$ 
D)  $\frac { x ^ { 2 } + 2 x - 6 } { x + 5 }$

Question 13

Solve the problem.
-A wire of length 3x is bent into the shape of a square. Express the area A of the square as a function of x. A) $\mathrm { A } ( \mathrm { x } ) = \frac { 3 } { 4 } \mathrm { x } ^ { 2 }$

Accepted Answer

B)  $A ( x ) = \frac { 9 } { 16 } x ^ { 2 }$ 
C)  $A ( x ) = \frac { 9 } { 8 } x ^ { 2 }$ 
D)  $A ( x ) = \frac { 1 } { 16 } x ^ { 2 }$ 
B)  $A ( x ) = \frac { 9 } { 16 } x ^ { 2 }$ 
C)  $A ( x ) = \frac { 9 } { 8 } x ^ { 2 }$ 
D)  $A ( x ) = \frac { 1 } { 16 } x ^ { 2 }$

Question 14

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: $f ( 3 ) = 6 ;$ Absolute minimum: $f ( 5 ) = 1$ 
B)  Absolute maximum: $f ( 7 ) = 4$; Absolute minimum: $f ( 0 ) = 2$ 
C)  Absolute maximum: $\mathrm { f } ( 3 ) = 6$; Absolute minimum: none 
D)  Absolute maximum: $f ( 3 ) = 6$; Absolute minimum: $f ( 0 ) = 2$ 
A)  Absolute maximum: $f ( 3 ) = 6 ;$ Absolute minimum: $f ( 5 ) = 1$ 
B)  Absolute maximum: $f ( 7 ) = 4$; Absolute minimum: $f ( 0 ) = 2$ 
C)  Absolute maximum: $\mathrm { f } ( 3 ) = 6$; Absolute minimum: none 
D)  Absolute maximum: $f ( 3 ) = 6$; Absolute minimum: $f ( 0 ) = 2$

Question 15

Solve the problem.
-Sue wants to put a rectangular garden on her property using 76 meters of fencing. There is a river that runs through her property so she decides to increase the size of the garden by using the river as one side of the
Rectangle. (Fencing is then needed only on the other three sides.) Let x represent the length of the side of the
Rectangle along the river. Express the garden's area as a function of x. A) $A ( x ) = 37 x - \frac { 1 } { 4 } x ^ { 2 }$

Accepted Answer

B)  $A ( x ) = 38 x ^ { 2 } - x$ 
C)  $A ( x ) = 38 x - \frac { 1 } { 2 } x ^ { 2 }$ 
D)  $A ( x ) = 39 x - 2 x ^ { 2 }$ 
B)  $A ( x ) = 38 x ^ { 2 } - x$ 
C)  $A ( x ) = 38 x - \frac { 1 } { 2 } x ^ { 2 }$ 
D)  $A ( x ) = 39 x - 2 x ^ { 2 }$

Question 16

If y varies directly as x, find a linear function which relates them.
-$$y = 5 \text { when } x = 40$$

Accepted Answer

A)  $f ( x ) = \frac { x } { 8 }$ 
B)  $f ( x ) = x + 35$ 
C)  $f ( x ) = \frac { x } { 5 }$ 
D)  $f ( x ) = 8 x$ 
A)  $f ( x ) = \frac { x } { 8 }$ 
B)  $f ( x ) = x + 35$ 
C)  $f ( x ) = \frac { x } { 5 }$ 
D)  $f ( x ) = 8 x$

Question 17

Solve the problem.
-The height s of a ball (in feet) thrown with an initial velocity of 60 feet per second from an initial height of 4 feet is given as a function of time $t$ (in seconds) by $\mathrm { s } ( \mathrm { t } ) = - 16 \mathrm { t } ^ { 2 } + 60 \mathrm { t } + 4$. What is the maximum height? Round to the nearest hundredth, if necessary.

Accepted Answer

A)  -37.25 ft 
B)  60.25 ft 
C)  69.63 ft 
D)  56.5 ft 
A)  -37.25 ft 
B)  60.25 ft 
C)  69.63 ft 
D)  56.5 ft

Question 18

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

Question 19

The graph of a function is given. Determine whether the function is increasing, decreasing, or constant on the given
interval.
-$$( - 6 , - 2.5 )$$

Accepted Answer

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

Question 20

Match the function with the graph that best describes the situation.
-A steel can in the shape of a right circular cylinder must be designed to hold 550 cubic centimeters of juice (see figure). It can be shown that the total surface area of the can (including the ends) is given by S(r) $$S ( r ) = 2 \pi r ^ { 2 } + \frac { 1,100 } { r }$$ where r is the radius of the can in centimeters. Using the TABLE feature of a graphing utility, find the radius
That minimizes the surface area (and thus the cost) of the can. Round to the nearest tenth of a centimeter.

Accepted Answer

A)  0 cm 
B)  5.6 cm 
C)  4.4 cm 
D)  3.6 cm 
A)  0 cm 
B)  5.6 cm 
C)  4.4 cm 
D)  3.6 cm

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

Solve the problem. -The gravitational attraction A between two masses varies inversely as the square of the distance between them. The force of attraction is 9 lb when the masses are 2 ft apart, what is the attraction when the masses are 6 ft Apart?

Suppose the point (2, 4) is on the graph of y = f(x). Find a point on the graph of the given function. -The reflection of the graph of y = f(x) across the y-axis

Answer the question about the given function. -Given the function $f ( x ) = 3 x ^ { 2 } - 6 x + 7$ , what is the domain of $f$ ?

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

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

Find the domain of the function. - $g ( x ) = \frac { 2 x } { x ^ { 2 } - 81 }$

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

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

Determine whether the relation represents a function. If it is a function, state the domain and range. - $\{(-1,-3),(-2,-2),(-2,0),(2,2),(14,4)\}$

Find the value for the function. -Find $f ( x + 1 )$ when $f ( x ) = \frac { x ^ { 2 } - 7 } { x + 4 }$

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

If y varies directly as x, find a linear function which relates them. - $y = 5 \text { when } x = 40$

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. - $( - 6 , - 2.5 )$

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

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

Solve the problem. -The gravitational attraction A between two masses varies inversely as the square of the distance between them. The force of attraction is 9 lb when the masses are 2 ft apart, what is the attraction when the masses are 6 ft Apart?

Suppose the point (2, 4) is on the graph of y = f(x). Find a point on the graph of the given function. -The reflection of the graph of y = f(x) across the y-axis

Answer the question about the given function. -Given the function f(x)=3x2−6x+7f ( x ) = 3 x ^ { 2 } - 6 x + 7f(x)=3x2−6x+7 , what is the domain of fff ?

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

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

Find the domain of the function. - g(x)=2xx2−81g ( x ) = \frac { 2 x } { x ^ { 2 } - 81 }g(x)=x2−812x​

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

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)=17x3f ( x ) = \frac { 1 } { 7 } x ^ { 3 }f(x)=71​x3 A) B) C) D)

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

Determine whether the relation represents a function. If it is a function, state the domain and range. - {(−1,−3),(−2,−2),(−2,0),(2,2),(14,4)}\{(-1,-3),(-2,-2),(-2,0),(2,2),(14,4)\}{(−1,−3),(−2,−2),(−2,0),(2,2),(14,4)}

Find the value for the function. -Find f(x+1)f ( x + 1 )f(x+1) when f(x)=x2−7x+4f ( x ) = \frac { x ^ { 2 } - 7 } { x + 4 }f(x)=x+4x2−7​

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

If y varies directly as x, find a linear function which relates them. - y=5 when x=40y = 5 \text { when } x = 40y=5 when x=40

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. - (−6,−2.5)( - 6 , - 2.5 )(−6,−2.5)

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 $f ( x ) = 3 x ^ { 2 } - 6 x + 7$ , what is the domain of $f$ ?

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

Find the domain of the function. - $g ( x ) = \frac { 2 x } { x ^ { 2 } - 81 }$

Determine whether the relation represents a function. If it is a function, state the domain and range. - $\{(-1,-3),(-2,-2),(-2,0),(2,2),(14,4)\}$

Find the value for the function. -Find $f ( x + 1 )$ when $f ( x ) = \frac { x ^ { 2 } - 7 } { x + 4 }$

If y varies directly as x, find a linear function which relates them. - $y = 5 \text { when } x = 40$

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. - $( - 6 , - 2.5 )$