Question 1

Find the domain and graph the function.
-$\mathrm{F}(\mathrm{x})=\sqrt{-\mathrm{x}}$

Accepted Answer

A)  D: $( - \infty , \infty )$
  
B)  D: $( - \infty , 0 )$
  
C)  D: $( - \infty , 0 ]$
  
D)  D: $[ 0 , \infty )$
  
A)  D: $( - \infty , \infty )$
  
B)  D: $( - \infty , 0 )$
  
C)  D: $( - \infty , 0 ]$
  
D)  D: $[ 0 , \infty )$

Question 2

Determine if the function is even, odd, or neither.
-f(x) = -6

Accepted Answer

A)  Even 
B)  Odd 
C)  Neither 
A)  Even 
B)  Odd 
C)  Neither

Question 3

Graph the function. Determine the symmetry, if any, of the function.
-$y = \frac { 1 } { x ^ { 3 } }$

Accepted Answer

A)  No symmetry
  
B)  Symmetric about the origin
  
C)  Symmetric about the $y$-axis
  
D)  Symmetric about the origin
  
A)  No symmetry
  
B)  Symmetric about the origin
  
C)  Symmetric about the $y$-axis
  
D)  Symmetric about the origin

Question 4

Determine if the function is even, odd, or neither.
-f(x) = (x - 5)(x + 8)

Accepted Answer

A)  Even 
B)  Odd 
C)  Neither 
A)  Even 
B)  Odd 
C)  Neither

Question 5

Find the formula for the function.
-A point P in the fourth quadrant lies on the graph of the function f(x) = -x2. Express the slope of the line joining P to the origin as a function of x.

Accepted Answer

A)  $m = - x$ 
B)  $m = \frac { 1 } { x }$ 
C)  $m = x$ 
D)  $m = - 2 x$ 
A)  $m = - x$ 
B)  $m = \frac { 1 } { x }$ 
C)  $m = x$ 
D)  $m = - 2 x$

Question 6

Determine whether or not the graph is a graph of a function of x.
-

Accepted Answer

A)  Function 
B)  Not a function 
A)  Function 
B)  Not a function

Question 7

Graph the function. Specify the intervals over which the function is increasing and the intervals where it is decreasing.
-$y = \frac { 1 } { x }$

Accepted Answer

A)  Decreasing $- \infty < x < 0$
 Increasing $0< x < \infty $ 
  
B)  Increasing $- \infty < x < 0$ and $0 < x <$
  
C)  Decreasing $- \infty < x < 0$ and $0 < x < \infty$
  
D)  Increasing $- \infty < x < 0$
Decreasing $0 < x < \infty $
  
A)  Decreasing $- \infty < x < 0$
 Increasing $0< x < \infty $ 
  
B)  Increasing $- \infty < x < 0$ and $0 < x <$
  
C)  Decreasing $- \infty < x < 0$ and $0 < x < \infty$
  
D)  Increasing $- \infty < x < 0$
Decreasing $0 < x < \infty $

Question 8

Find a formula for the function graphed.
-

Accepted Answer

A)  $f ( x ) = \left\{ \begin{array} { l l } 1 - x & x  2 \end{array} \right.$ 
C)  $f ( x ) = \left\{ \begin{array} { l l } 1 - x , & x \leq 2 \ 7 & x > 2 \end{array} \right.$ 
D)  $f ( x ) = \left\{ \begin{array} { l l } 1 + x & x \leq 2 \ 7 & x > 2 \end{array} \right.$ 
A)  $f ( x ) = \left\{ \begin{array} { l l } 1 - x & x  2 \end{array} \right.$ 
C)  $f ( x ) = \left\{ \begin{array} { l l } 1 - x , & x \leq 2 \ 7 & x > 2 \end{array} \right.$ 
D)  $f ( x ) = \left\{ \begin{array} { l l } 1 + x & x \leq 2 \ 7 & x > 2 \end{array} \right.$

Question 9

Determine if the function is even, odd, or neither.
-$f ( x ) = 2 x ^ { 5 } - 7 x ^ { 3 }$

Accepted Answer

A)  Even 
B)  Odd 
C)  Neither 
A)  Even 
B)  Odd 
C)  Neither

Question 10

Express the given function as a composite of functions f and g such that y = f(g(x)).
-Let $g ( x ) = \sqrt { x }$. Find a function $y = f ( x )$ so that $( f \circ g ) ( x ) = | x |$.

Accepted Answer

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

Question 11

Graph the function. Specify the intervals over which the function is increasing and the intervals where it is decreasing.
-$$y = \sqrt { - x }$$

Accepted Answer

A)  Decreasing $- \infty < x \leq 0$
  
B)  Increasing $- \infty < x \leq 0$
  
C)  Decreasing $0 \leq x < \infty$
  
D)  Decreasing $- \infty < x \leq 0$
Increasing $0\leq  x \leq \infty$
  
A)  Decreasing $- \infty < x \leq 0$
  
B)  Increasing $- \infty < x \leq 0$
  
C)  Decreasing $0 \leq x < \infty$
  
D)  Decreasing $- \infty < x \leq 0$
Increasing $0\leq  x \leq \infty$

Question 12

Find the formula for the function.
-A point P in the first quadrant lies on the graph of the function f(x) = x2. Express the slope of the line joining P to the origin as a function of x.

Accepted Answer

A)  $m = x$ 
B)  $m = \frac { 1 } { x }$ 
C)  $m = \frac { 2 } { x }$ 
D)  $m = 2 x$ 
A)  $m = x$ 
B)  $m = \frac { 1 } { x }$ 
C)  $m = \frac { 2 } { x }$ 
D)  $m = 2 x$

Question 13

The figure shown here shows a rectangle inscribed in an isosceles right triangle whose hypotenuse is 8 units long. Express the area A of the rectangle in terms of x.

Accepted Answer

A)  A(x) = 2x(4 - x) 
B)  A(x) = 2x(x - 4) 
C)  A(x) = 2x2 
D)  A(x) = x(4 - x) 
A)  A(x) = 2x(4 - x) 
B)  A(x) = 2x(x - 4) 
C)  A(x) = 2x2 
D)  A(x) = x(4 - x)

Question 14

Determine whether or not the graph is a graph of a function of x.
-

Accepted Answer

A)  Function 
B)  Not a function 
A)  Function 
B)  Not a function

Question 15

Graph the function. Determine the symmetry, if any, of the function.
-$y=-2 \sqrt{x}$

Accepted Answer

A)  Symmetric about the $x$-axis
  
B)  No symmetry
  
C)  No symmetry
  
D)  Symmetric about the $x$-axis
  
A)  Symmetric about the $x$-axis
  
B)  No symmetry
  
C)  No symmetry
  
D)  Symmetric about the $x$-axis

Question 16

Express the given function as a composite of functions f and g such that y = f(g(x)).
-The accompanying figure shows the graph of $y = x ^ { 2 }$ shifted to a new position. Write the equation for the new graph.

Accepted Answer

A)  $y = ( x - 5 ) ^ { 2 }$ 
B)  $y = x ^ { 2 } - 5$ 
C)  $y = x ^ { 2 } + 5$ 
D)  $y = ( x + 5 ) ^ { 2 }$ 
A)  $y = ( x - 5 ) ^ { 2 }$ 
B)  $y = x ^ { 2 } - 5$ 
C)  $y = x ^ { 2 } + 5$ 
D)  $y = ( x + 5 ) ^ { 2 }$

Question 17

Find the domain and range of the function.
-$$g ( z ) = \sqrt { 1 - z ^ { 2 } }$$

Accepted Answer

A)  D: $( - 1,1 )$, R: $( - 1,1 )$ 
B)  D: $[ 0 , \infty )$, R: $( - \infty , \infty )$ 
C)  D: $[ - 1,1 ]$, R: $[ 0,1 ]$ 
D)  D: $( - \infty , \infty ) , R : ( 0,1 )$ 
A)  D: $( - 1,1 )$, R: $( - 1,1 )$ 
B)  D: $[ 0 , \infty )$, R: $( - \infty , \infty )$ 
C)  D: $[ - 1,1 ]$, R: $[ 0,1 ]$ 
D)  D: $( - \infty , \infty ) , R : ( 0,1 )$

Question 18

Find the formula for the function.
-Express the area of a square as a function of its side length x.

Accepted Answer

A)  A = 2x 
B) $\mathrm{A}=\mathrm{x}^{4}$ 
C)  $A=x^{2}$ 
D)  A = 4x 
A)  A = 2x 
B) $\mathrm{A}=\mathrm{x}^{4}$ 
C)  $A=x^{2}$ 
D)  A = 4x

Question 19

Find the domain and range of the function.
-$$f ( x ) = 4 - x ^ { 2 }$$

Accepted Answer

A)  D: $( - \infty , \infty ) , R : ( - \infty , 4 ]$ 
B)  D: $( - \infty , \infty ) , R : ( - \infty , \infty )$ 
C)  D: $( - \infty , 4 ] , R : ( - \infty , \infty )$ 
D)  D: $( - \infty , \infty )$, R: $[ 4 , \infty )$ 
A)  D: $( - \infty , \infty ) , R : ( - \infty , 4 ]$ 
B)  D: $( - \infty , \infty ) , R : ( - \infty , \infty )$ 
C)  D: $( - \infty , 4 ] , R : ( - \infty , \infty )$ 
D)  D: $( - \infty , \infty )$, R: $[ 4 , \infty )$

Question 20

Graph the function. Determine the symmetry, if any, of the function.
-$y=(-x)^{3 / 2}$

Accepted Answer

A)  Symmetric about the $y$-axis
  
B)  No symmetry
  
C)  No symmetry
  
D)  Symmetric about the $y$-axis
  
A)  Symmetric about the $y$-axis
  
B)  No symmetry
  
C)  No symmetry
  
D)  Symmetric about the $y$-axis

Find the domain and graph the function. - $\mathrm{F}(\mathrm{x})=\sqrt{-\mathrm{x}}$ $Find the domain and graph the function. - \mathrm{F}(\mathrm{x})=\sqrt{-\mathrm{x}}$

Determine if the function is even, odd, or neither. -f(x) = -6

Graph the function. Determine the symmetry, if any, of the function. - $y = \frac { 1 } { x ^ { 3 } }$ $Graph the function. Determine the symmetry, if any, of the function. - y = \frac { 1 } { x ^ { 3 } }$

Determine if the function is even, odd, or neither. -f(x) = (x - 5)(x + 8)

Find the formula for the function. -A point P in the fourth quadrant lies on the graph of the function f(x) = -x2. Express the slope of the line joining P to the origin as a function of x.

Determine whether or not the graph is a graph of a function of x. -

Graph the function. Specify the intervals over which the function is increasing and the intervals where it is decreasing. - $y = \frac { 1 } { x }$ $Graph the function. Specify the intervals over which the function is increasing and the intervals where it is decreasing. - y = \frac { 1 } { x }$

Find a formula for the function graphed. -

Determine if the function is even, odd, or neither. - $f ( x ) = 2 x ^ { 5 } - 7 x ^ { 3 }$

Express the given function as a composite of functions f and g such that y = f(g(x)). -Let $g ( x ) = \sqrt { x }$ . Find a function $y = f ( x )$ so that $( f \circ g ) ( x ) = | x |$ .

Graph the function. Specify the intervals over which the function is increasing and the intervals where it is decreasing. - $y = \sqrt { - x }$ $Graph the function. Specify the intervals over which the function is increasing and the intervals where it is decreasing. - y = \sqrt { - x }$

Find the formula for the function. -A point P in the first quadrant lies on the graph of the function f(x) = x2. Express the slope of the line joining P to the origin as a function of x.

The figure shown here shows a rectangle inscribed in an isosceles right triangle whose hypotenuse is 8 units long. Express the area A of the rectangle in terms of x.

Determine whether or not the graph is a graph of a function of x. -

Graph the function. Determine the symmetry, if any, of the function. - $y=-2 \sqrt{x}$ $Graph the function. Determine the symmetry, if any, of the function. - y=-2 \sqrt{x}$

Find the domain and range of the function. - $g ( z ) = \sqrt { 1 - z ^ { 2 } }$

Find the formula for the function. -Express the area of a square as a function of its side length x.

Find the domain and range of the function. - $f ( x ) = 4 - x ^ { 2 }$

Graph the function. Determine the symmetry, if any, of the function. - $y=(-x)^{3 / 2}$ $Graph the function. Determine the symmetry, if any, of the function. - y=(-x)^{3 / 2}$

Limits and Derivatives

Differentiation

Applications of Derivatives

Integration

Applications of Definite Integrals

Integrals and Transcendental Functions

Techniques of Integration

First-Order Differential Equations

Infinite Sequences and Series

Filters

Exam 1: Functions

Find the domain and graph the function. - F(x)=−x\mathrm{F}(\mathrm{x})=\sqrt{-\mathrm{x}}F(x)=−x​

Determine if the function is even, odd, or neither. -f(x) = -6

Graph the function. Determine the symmetry, if any, of the function. - y=1x3y = \frac { 1 } { x ^ { 3 } }y=x31​

Determine if the function is even, odd, or neither. -f(x) = (x - 5)(x + 8)

Find the formula for the function. -A point P in the fourth quadrant lies on the graph of the function f(x) = -x2. Express the slope of the line joining P to the origin as a function of x.

Determine whether or not the graph is a graph of a function of x. -

Graph the function. Specify the intervals over which the function is increasing and the intervals where it is decreasing. - y=1xy = \frac { 1 } { x }y=x1​

Find a formula for the function graphed. -

Determine if the function is even, odd, or neither. - f(x)=2x5−7x3f ( x ) = 2 x ^ { 5 } - 7 x ^ { 3 }f(x)=2x5−7x3

Express the given function as a composite of functions f and g such that y = f(g(x)). -Let g(x)=xg ( x ) = \sqrt { x }g(x)=x​ . Find a function y=f(x)y = f ( x )y=f(x) so that (f∘g)(x)=∣x∣( f \circ g ) ( x ) = | x |(f∘g)(x)=∣x∣ .

Graph the function. Specify the intervals over which the function is increasing and the intervals where it is decreasing. - y=−xy = \sqrt { - x }y=−x​

Find the formula for the function. -A point P in the first quadrant lies on the graph of the function f(x) = x2. Express the slope of the line joining P to the origin as a function of x.

The figure shown here shows a rectangle inscribed in an isosceles right triangle whose hypotenuse is 8 units long. Express the area A of the rectangle in terms of x.

Determine whether or not the graph is a graph of a function of x. -

Graph the function. Determine the symmetry, if any, of the function. - y=−2xy=-2 \sqrt{x}y=−2x​

Express the given function as a composite of functions f and g such that y = f(g(x)). -The accompanying figure shows the graph of y=x2y = x ^ { 2 }y=x2 shifted to a new position. Write the equation for the new graph.

Find the domain and range of the function. - g(z)=1−z2g ( z ) = \sqrt { 1 - z ^ { 2 } }g(z)=1−z2​

Find the formula for the function. -Express the area of a square as a function of its side length x.

Find the domain and range of the function. - f(x)=4−x2f ( x ) = 4 - x ^ { 2 }f(x)=4−x2

Graph the function. Determine the symmetry, if any, of the function. - y=(−x)3/2y=(-x)^{3 / 2}y=(−x)3/2

Limits and Derivatives

Differentiation

Applications of Derivatives

Integration

Applications of Definite Integrals

Integrals and Transcendental Functions

Techniques of Integration

First-Order Differential Equations

Infinite Sequences and Series

Filters

Find the domain and graph the function. - $\mathrm{F}(\mathrm{x})=\sqrt{-\mathrm{x}}$ $Find the domain and graph the function. - \mathrm{F}(\mathrm{x})=\sqrt{-\mathrm{x}}$

Graph the function. Determine the symmetry, if any, of the function. - $y = \frac { 1 } { x ^ { 3 } }$ $Graph the function. Determine the symmetry, if any, of the function. - y = \frac { 1 } { x ^ { 3 } }$

Graph the function. Specify the intervals over which the function is increasing and the intervals where it is decreasing. - $y = \frac { 1 } { x }$ $Graph the function. Specify the intervals over which the function is increasing and the intervals where it is decreasing. - y = \frac { 1 } { x }$

Determine if the function is even, odd, or neither. - $f ( x ) = 2 x ^ { 5 } - 7 x ^ { 3 }$

Express the given function as a composite of functions f and g such that y = f(g(x)). -Let $g ( x ) = \sqrt { x }$ . Find a function $y = f ( x )$ so that $( f \circ g ) ( x ) = | x |$ .

Graph the function. Specify the intervals over which the function is increasing and the intervals where it is decreasing. - $y = \sqrt { - x }$ $Graph the function. Specify the intervals over which the function is increasing and the intervals where it is decreasing. - y = \sqrt { - x }$

Graph the function. Determine the symmetry, if any, of the function. - $y=-2 \sqrt{x}$ $Graph the function. Determine the symmetry, if any, of the function. - y=-2 \sqrt{x}$

Find the domain and range of the function. - $g ( z ) = \sqrt { 1 - z ^ { 2 } }$

Find the domain and range of the function. - $f ( x ) = 4 - x ^ { 2 }$

Graph the function. Determine the symmetry, if any, of the function. - $y=(-x)^{3 / 2}$ $Graph the function. Determine the symmetry, if any, of the function. - y=(-x)^{3 / 2}$