Question 1

Determine whether (f ∘ g)(x) = x and whether (g ∘ f)(x) = x.
-$$f ( x ) = x ^ { 3 } + 7 , g ( x ) = \sqrt [ 3 ] { x - 7 }$$

Accepted Answer

A)  Yes, no 
B)  No, yes 
C)  No, no 
D)  Yes, yes 
A)  Yes, no 
B)  No, yes 
C)  No, no 
D)  Yes, yes

Question 2

The graph of a linear function f is shown. Identify the slope, y-intercept, and x-intercept.
-

Accepted Answer

A)  $\frac { 1 } { 4 } ; 2 , - 8$ 
B)  $4 ; 2 , - 8$ 
C)  $\frac { 1 } { 4 } ; - 8,2$ 
D)  $4 ; - 8,2$ 
A)  $\frac { 1 } { 4 } ; 2 , - 8$ 
B)  $4 ; 2 , - 8$ 
C)  $\frac { 1 } { 4 } ; - 8,2$ 
D)  $4 ; - 8,2$

Question 3

Graph the linear function and give the domain and the range. If the function is a constant function, identify it as such.
-$f(x)=\frac{1}{5} x+3$

Accepted Answer

A)  $\mathrm { D } = ( - \infty , \infty ) , \mathrm { R } = ( - \infty , \infty )$
  
B)  $\mathrm { D } = ( - \infty , \infty ) , \mathrm { R } = ( - \infty , \infty )$
  
C)  $\mathrm { D } = ( - \infty , \infty ) , \mathrm { R } = ( - \infty , \infty )$
  
D)  $\mathrm { D } = ( - \infty , \infty ) , \mathrm { R } = ( - \infty , \infty )$
  
A)  $\mathrm { D } = ( - \infty , \infty ) , \mathrm { R } = ( - \infty , \infty )$
  
B)  $\mathrm { D } = ( - \infty , \infty ) , \mathrm { R } = ( - \infty , \infty )$
  
C)  $\mathrm { D } = ( - \infty , \infty ) , \mathrm { R } = ( - \infty , \infty )$
  
D)  $\mathrm { D } = ( - \infty , \infty ) , \mathrm { R } = ( - \infty , \infty )$

Question 4

Use the graph to solve the problem.
-At what times was the temperature higher than $77 ^ { \circ } \mathrm { F }$ ?

Accepted Answer

A)  after 12 p.m. 
B)  from 12 p.m. until 3 p.m. 
C)  from 12 p.m. until 1 p.m. 
D)  from 11 a.m. until 3 p.m. 
A)  after 12 p.m. 
B)  from 12 p.m. until 3 p.m. 
C)  from 12 p.m. until 1 p.m. 
D)  from 11 a.m. until 3 p.m.

Question 5

Find the specified domain.
-Find the domain of $\left( \frac { f } { g } \right) ( x )$ when $f ( x ) = \sqrt { 5 x - 7 }$ and $g ( x ) = \frac { 1 } { x }$

Accepted Answer

A)  $( - \infty , 0 ) \cup ( 0 , \infty )$ 
B)  $\left[ \frac { 7 } { 5 } , \infty \right]$ 
C)  $\left[ - \frac { 7 } { 5 } , 0 \right] \cup ( 0 , \infty )$ 
D)  $\left[ - \frac { 7 } { 5 } , \infty \right)$ 
A)  $( - \infty , 0 ) \cup ( 0 , \infty )$ 
B)  $\left[ \frac { 7 } { 5 } , \infty \right]$ 
C)  $\left[ - \frac { 7 } { 5 } , 0 \right] \cup ( 0 , \infty )$ 
D)  $\left[ - \frac { 7 } { 5 } , \infty \right)$

Determine whether (f ∘ g)(x) = x and whether (g ∘ f)(x) = x. - $f ( x ) = x ^ { 3 } + 7 , g ( x ) = \sqrt [ 3 ] { x - 7 }$

The graph of a linear function f is shown. Identify the slope, y-intercept, and x-intercept. -

Graph the linear function and give the domain and the range. If the function is a constant function, identify it as such. - $f(x)=\frac{1}{5} x+3$ $Graph the linear function and give the domain and the range. If the function is a constant function, identify it as such. - f(x)=\frac{1}{5} x+3$

Use the graph to solve the problem. -At what times was the temperature higher than $77 ^ { \circ } \mathrm { F }$ ?

Find the specified domain. -Find the domain of $\left( \frac { f } { g } \right) ( x )$ when $f ( x ) = \sqrt { 5 x - 7 }$ and $g ( x ) = \frac { 1 } { x }$

Equations and Inequalities

Polynomial and Rational Functions

Inverse, Exponential, and Logarithmic Functions

Trigonometric Functions

The Circular Functions and Their Graphs

Trigonometric Identities and Equations

Applications of Trigonometry

Systems and Matrices

Analytic Geometry

Further Topics in Algebra

Review of Basic Concepts

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Exam 2: Graphs and Functions

Determine whether (f ∘ g)(x) = x and whether (g ∘ f)(x) = x. - f(x)=x3+7,g(x)=x−73f ( x ) = x ^ { 3 } + 7 , g ( x ) = \sqrt [ 3 ] { x - 7 }f(x)=x3+7,g(x)=3x−7​