Question 1

Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting.
-$$f ( x ) = | x | - 3$$

Accepted Answer

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

Question 2

Determine algebraically whether the function is even, odd, or neither.
-$$f ( x ) = - 8 x ^ { 2 } - 9$$

Accepted Answer

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

Question 3

The function f is one-to-one. State the domain and the range of f and fS1U1P1-1S1S1P0. Write the domain and range in set-builder
notation.
-$$f ( x ) = - 4 x + 5$$

Accepted Answer

A) $ f(x) $ : D is all real numbers, $ R=\{y \mid y>5\} $; $ f^{-1}(x) $ : $ D $ is all real numbers, $ R=\{y \mid y - 4 \} , R$ is all real numbers; $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) : \mathrm { D } = \{ \mathrm { x } \mid \mathrm { x } - 4 \} , R = \{ y \mid y > 5 \}$; $$f ^ { - 1 } ( x ) : D = \{ x \mid x < - 4 \} , R = \{ y \mid y < 5 \}$$ A) $ f(x) $ : D is all real numbers, $ R=\{y \mid y>5\} $; $ f^{-1}(x) $ : $ D $ is all real numbers, $ R=\{y \mid y - 4 \} , R$ is all real numbers; $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) : \mathrm { D } = \{ \mathrm { x } \mid \mathrm { x } - 4 \} , R = \{ y \mid y > 5 \}$; $$f ^ { - 1 } ( x ) : D = \{ x \mid x < - 4 \} , R = \{ y \mid y < 5 \}$$

Question 4

Find the rule that defines each piecewise-defined function.
-

Accepted Answer

A)  $f ( x ) = \left\{ \begin{array} { l l } - \frac { 1 } { 2 } x & \text { if } - 4 < x < 0 \ x & \text { if } 0 < x < 3 \end{array} \right.$ 
B)  $f ( x ) = \left\{ \begin{array} { l l } - 2 x & \text { if } - 4 \leq x \leq 0 \ x & \text { if } 0 < x \leq 3 \end{array} \right.$ 
C) $f ( x ) = \left\{ \begin{array} { l l } - \frac { 1 } { 2 } x & \text { if } - 4 \leq x \leq 0 \ x & \text { if } 0 < x \leq 3 \end{array} \right.$ 
D)  $f ( x ) = \left\{ \begin{array} { l l } \frac { 1 } { 2 } x & \text { if } - 4 < x < 0 \ x & \text { if } 0 < x < 3 \end{array} \right.$ 
A)  $f ( x ) = \left\{ \begin{array} { l l } - \frac { 1 } { 2 } x & \text { if } - 4 < x < 0 \ x & \text { if } 0 < x < 3 \end{array} \right.$ 
B)  $f ( x ) = \left\{ \begin{array} { l l } - 2 x & \text { if } - 4 \leq x \leq 0 \ x & \text { if } 0 < x \leq 3 \end{array} \right.$ 
C) $f ( x ) = \left\{ \begin{array} { l l } - \frac { 1 } { 2 } x & \text { if } - 4 \leq x \leq 0 \ x & \text { if } 0 < x \leq 3 \end{array} \right.$ 
D)  $f ( x ) = \left\{ \begin{array} { l l } \frac { 1 } { 2 } x & \text { if } - 4 < x < 0 \ x & \text { if } 0 < x < 3 \end{array} \right.$

Question 5

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

Accepted Answer

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

Question 6

Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting.
-$f(x)=6 \sqrt{x}$

Accepted Answer

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

Question 7

For the given functions f and g, find the requested function and state its domain. Write the domain in interval notation.
-$f ( x ) = 5 x ^ { 3 } + 3 ; g ( x ) = 3 x ^ { 2 } + 2 ; \quad$ Find $f \cdot g$.

Accepted Answer

A)  $( f \cdot g ) ( x ) = 15 x ^ { 5 } + 10 x ^ { 3 } + 9 x ^ { 2 } + 6 ; ( \infty , 0 ) \cup ( 0 , \infty )$ 
B)  $( f \cdot g ) ( x ) = 5 x ^ { 3 } + 3 x ^ { 2 } + 6 ; ( \infty , \infty )$ 
C)  $( \mathrm { f } \cdot \mathrm { g } ) ( \mathrm { x } ) = 15 \mathrm { x } ^ { 5 } + 10 \mathrm { x } ^ { 3 } + 9 \mathrm { x } ^ { 2 } + 6 ; ( \infty , \infty )$ 
D)  $( f \cdot g ) ( x ) = 15 x ^ { 6 } + 10 x ^ { 3 } + 9 x ^ { 2 } + 6 ; ( \infty , \infty )$ 
A)  $( f \cdot g ) ( x ) = 15 x ^ { 5 } + 10 x ^ { 3 } + 9 x ^ { 2 } + 6 ; ( \infty , 0 ) \cup ( 0 , \infty )$ 
B)  $( f \cdot g ) ( x ) = 5 x ^ { 3 } + 3 x ^ { 2 } + 6 ; ( \infty , \infty )$ 
C)  $( \mathrm { f } \cdot \mathrm { g } ) ( \mathrm { x } ) = 15 \mathrm { x } ^ { 5 } + 10 \mathrm { x } ^ { 3 } + 9 \mathrm { x } ^ { 2 } + 6 ; ( \infty , \infty )$ 
D)  $( f \cdot g ) ( x ) = 15 x ^ { 6 } + 10 x ^ { 3 } + 9 x ^ { 2 } + 6 ; ( \infty , \infty )$

Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting. - $f ( x ) = | x | - 3$

Determine algebraically whether the function is even, odd, or neither. - $f ( x ) = - 8 x ^ { 2 } - 9$

The function f is one-to-one. State the domain and the range of f and f^-1. Write the domain and range in set-builder notation. - $f ( x ) = - 4 x + 5$

Find the rule that defines each piecewise-defined function. -

For the given functions f and g, find the requested function and state its domain. Write the domain in interval notation. - $f ( x ) = 5 x ^ { 3 } + 3 ; g ( x ) = 3 x ^ { 2 } + 2 ; \quad$ Find $f \cdot g$ .

Equations, Inequalities, and Applications

The Rectangular Coordinate System, Lines, and Circles

Polynomial and Rational Functions

Exponential and Logarithmic Functions and Equations

Conic Sections

Systems of Equations and Inequalities

Matrices

Sequences and Series; Counting and Probability

Math Exercises: Sets, Intervals, Absolute Value, and Properties

Filters

Exam 3: Functions

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)=∣x∣−3f ( x ) = | x | - 3f(x)=∣x∣−3

Determine algebraically whether the function is even, odd, or neither. - f(x)=−8x2−9f ( x ) = - 8 x ^ { 2 } - 9f(x)=−8x2−9

The function f is one-to-one. State the domain and the range of f and f-1. Write the domain and range in set-builder notation. - f(x)=−4x+5f ( x ) = - 4 x + 5f(x)=−4x+5

Find the rule that defines each piecewise-defined function. -

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)=x−3f(x)=\sqrt{x-3}f(x)=x−3​

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)=6xf(x)=6 \sqrt{x}f(x)=6x​

For the given functions f and g, find the requested function and state its domain. Write the domain in interval notation. - f(x)=5x3+3;g(x)=3x2+2;f ( x ) = 5 x ^ { 3 } + 3 ; g ( x ) = 3 x ^ { 2 } + 2 ; \quadf(x)=5x3+3;g(x)=3x2+2; Find f⋅gf \cdot gf⋅g .

Equations, Inequalities, and Applications

The Rectangular Coordinate System, Lines, and Circles

Polynomial and Rational Functions

Exponential and Logarithmic Functions and Equations

Conic Sections

Systems of Equations and Inequalities

Matrices

Sequences and Series; Counting and Probability

Math Exercises: Sets, Intervals, Absolute Value, and Properties

Filters

Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting. - $f ( x ) = | x | - 3$

Determine algebraically whether the function is even, odd, or neither. - $f ( x ) = - 8 x ^ { 2 } - 9$

The function f is one-to-one. State the domain and the range of f and f^-1. Write the domain and range in set-builder notation. - $f ( x ) = - 4 x + 5$

For the given functions f and g, find the requested function and state its domain. Write the domain in interval notation. - $f ( x ) = 5 x ^ { 3 } + 3 ; g ( x ) = 3 x ^ { 2 } + 2 ; \quad$ Find $f \cdot g$ .