Question 1

Describe how the graph of the equation relates to the graph of y $y = x ^ { 2 }$
-$$f ( x ) = 5 x ^ { 2 }$$

Accepted Answer

A)  a translation 5 units up 
B)  a horizontal stretch by a factor of 5 
C)  a vertical stretch by a factor of 5 
D)  a translation 5 units to the right 
A)  a translation 5 units up 
B)  a horizontal stretch by a factor of 5 
C)  a vertical stretch by a factor of 5 
D)  a translation 5 units to the right

Question 2

Determine the intervals of the domain over which the function is continuous.
-$P(-1,-3)$

Accepted Answer

A)  $( - \infty , - 3 ) \cup ( - 3 , \infty )$ 
B)  $( - \infty , - 1 ] \cup [ - 1 , \infty )$ 
C)  $( - \infty , - 1 ) \cup ( - 1 , \infty )$ 
D)  $( - \infty , \infty )$ 
A)  $( - \infty , - 3 ) \cup ( - 3 , \infty )$ 
B)  $( - \infty , - 1 ] \cup [ - 1 , \infty )$ 
C)  $( - \infty , - 1 ) \cup ( - 1 , \infty )$ 
D)  $( - \infty , \infty )$

Question 3

Evaluate the function.
-Find $g ( a - 1 )$ when $g ( x ) = 2 x + 5$

Accepted Answer

A)  $2 a + 3$ 
B)  $2 a + 1$ 
C)  $2 a + 5$ 
D)  $\frac { 1 } { 2 } a + 5$ 
A)  $2 a + 3$ 
B)  $2 a + 1$ 
C)  $2 a + 5$ 
D)  $\frac { 1 } { 2 } a + 5$

Question 4

Decide whether the relation defines a function.
-

Accepted Answer

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

Question 5

Graph the equation by plotting points.
-$y=x^{2}-2$

Accepted Answer

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

Question 6

Graph the point symmetric to the given point.
-$$\text { Plot the point } ( - 2,9 ) \text {, then plot the point that is symmetric to } ( - 2,9 ) \text { with respect to the } y \text {-axis. }$$

Accepted Answer

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

Question 7

Find the slope of the line satisfying the given conditions.
-through $( 1 , - 7 )$ and $( - 9,9 )$

Accepted Answer

A)  $- \frac { 8 } { 5 }$ 
B)  $- \frac { 5 } { 8 }$ 
C)  $\frac { 5 } { 8 }$ 
D)  $\frac { 8 } { 5 }$ 
A)  $- \frac { 8 } { 5 }$ 
B)  $- \frac { 5 } { 8 }$ 
C)  $\frac { 5 } { 8 }$ 
D)  $\frac { 8 } { 5 }$

Question 8

Decide whether the relation defines a function.
-

Accepted Answer

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

Question 9

For the given functions f and g , find the indicated composition.
-$$\begin{array} { l } 
f ( x ) = \sqrt { x + 8 } , \quad g ( x ) = 8 x - 12 \
( f g g ) ( x )
\end{array}$$

Accepted Answer

A)  $2 \sqrt { 2 x - 1 }$ 
B)  $8 \sqrt { x + 8 } - 12$ 
C)  $2 \sqrt { 2 x + 1 }$ 
D)  $8 \sqrt { x - 4 }$ 
A)  $2 \sqrt { 2 x - 1 }$ 
B)  $8 \sqrt { x + 8 } - 12$ 
C)  $2 \sqrt { 2 x + 1 }$ 
D)  $8 \sqrt { x - 4 }$

Question 10

Graph the function.
-$f(x)=\left\{\begin{array}{ll}
2, & \text { if } x>-5 \
-2, & \text { if } x \leq-5
\end{array}\right.$

Accepted Answer

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

Question 11

Match the description with the correct symbolic expression.
-a linear function whose graph has a slope of 8

Accepted Answer

A)  $8 x - 8 y = 6$ 
B)  $y = 8 x + 6$ 
C)  $x = 8$ 
D)  $f ( x ) = - 10 x + 8$ 
A)  $8 x - 8 y = 6$ 
B)  $y = 8 x + 6$ 
C)  $x = 8$ 
D)  $f ( x ) = - 10 x + 8$

Question 12

Determine whether the three points are the vertices of a right triangle.
-(-5, 2), (0, 2), (0, 4)

Accepted Answer

A)  Yes 
B)  No 
A)  Yes 
B)  No

Question 13

Find the specified domain.
-Use the graphs to find the value of $\left( \frac { f } { g } \right) ( 3 )$.

Accepted Answer

A)  $- 2$ 
B)  $- 1$ 
C)  1 
D)  undefined 
A)  $- 2$ 
B)  $- 1$ 
C)  1 
D)  undefined

Question 14

Graph the function.
-$f(x)=7 x^{2}$

Accepted Answer

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

Question 15

Provide an appropriate response.
-If a vertical line is drawn through the point (-5, 6), where will it intersect the x-axis?

Accepted Answer

A)  (0, 6) 
B)  (0, -5) 
C)  (6, 0) 
D)  (-5, 0) 
A)  (0, 6) 
B)  (0, -5) 
C)  (6, 0) 
D)  (-5, 0)

Question 16

The graph of $\mathrm { y } _ { 1 }$ is shown in the standard viewing window. Which is the only choice that could possibly be the solution of the equation $\mathrm { y } _ { 1 } = 0$ ?

- 
$$- 90 , - \frac { 91 } { 10 } , \frac { 91 } { 10 } , 85$$

Accepted Answer

A)  $\frac { 91 } { 10 }$ 
B)  $- 90$ 
C)  $- \frac { 91 } { 10 }$ 
D)  85 
A)  $\frac { 91 } { 10 }$ 
B)  $- 90$ 
C)  $- \frac { 91 } { 10 }$ 
D)  85

Question 17

Find the requested function value.
-Find $( g \circ f ) ( - 1 )$ when $f ( x ) = \frac { x - 7 } { 8 }$ and $g ( x ) = 8 x + 1$

Accepted Answer

A)  $- 7$ 
B)  7 
C)  $- 9$ 
D)  $- \frac { 7 } { 4 }$ 
A)  $- 7$ 
B)  7 
C)  $- 9$ 
D)  $- \frac { 7 } { 4 }$

Question 18

Graph the line and give the domain and the range.
-$x+1=0$

Accepted Answer

A)  $D=\{-1\}, R=(-\infty, \infty)$
  
B)  $D=(-\infty, \infty), R=\{-1\}$
  
C)  $\mathrm { D } = ( - \infty , \infty ) , \mathrm { R } = ( - \infty , \infty )$
  
D)  $D = ( - \infty , \infty ) , R = \{ - 1 \}$
  
A)  $D=\{-1\}, R=(-\infty, \infty)$
  
B)  $D=(-\infty, \infty), R=\{-1\}$
  
C)  $\mathrm { D } = ( - \infty , \infty ) , \mathrm { R } = ( - \infty , \infty )$
  
D)  $D = ( - \infty , \infty ) , R = \{ - 1 \}$

Question 19

Graph the line described.
-$$\text { through } ( - 2 , - 4 ) ; m = 5$$

Accepted Answer

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

Question 20

Give the domain and range of the relation.
-$x y = - 7$

Accepted Answer

A)  domain: $( - \infty , 0 ) \cup ( 0 , \infty )$; range: $( - \infty , 0 ) \cup ( 0 , \infty )$ 
B)  domain: $[ 0 , \infty )$; range: $( - \infty , \infty )$ 
C)  domain: $( - \infty , \infty )$; range: $( - \infty , \infty )$ 
D)  domain: $( - \infty , 0 ) \cup ( 0 , \infty )$; range: $[ 0 , \infty )$ 
A)  domain: $( - \infty , 0 ) \cup ( 0 , \infty )$; range: $( - \infty , 0 ) \cup ( 0 , \infty )$ 
B)  domain: $[ 0 , \infty )$; range: $( - \infty , \infty )$ 
C)  domain: $( - \infty , \infty )$; range: $( - \infty , \infty )$ 
D)  domain: $( - \infty , 0 ) \cup ( 0 , \infty )$; range: $[ 0 , \infty )$

Describe how the graph of the equation relates to the graph of y $y = x ^ { 2 }$ - $f ( x ) = 5 x ^ { 2 }$

Determine the intervals of the domain over which the function is continuous. - $P(-1,-3)$

Evaluate the function. -Find $g ( a - 1 )$ when $g ( x ) = 2 x + 5$

Decide whether the relation defines a function. -

Graph the equation by plotting points. - $y=x^{2}-2$ $Graph the equation by plotting points. - y=x^{2}-2$

Find the slope of the line satisfying the given conditions. -through $( 1 , - 7 )$ and $( - 9,9 )$

Decide whether the relation defines a function. -

For the given functions f and g , find the indicated composition. - f(x)=,g(x)=8x-12 (fgg)(x)

Graph the function. - $f(x)=\left\{\begin{array}{ll}2, & \text { if } x>-5 \\-2, & \text { if } x \leq-5\end{array}\right.$ $Graph the function. - f(x)=\left\{\begin{array}{ll} 2, & \text { if } x>-5 \\ -2, & \text { if } x \leq-5 \end{array}\right.$

Match the description with the correct symbolic expression. -a linear function whose graph has a slope of 8

Determine whether the three points are the vertices of a right triangle. -(-5, 2), (0, 2), (0, 4)

Find the specified domain. -Use the graphs to find the value of $\left( \frac { f } { g } \right) ( 3 )$ . $Find the specified domain. -Use the graphs to find the value of \left( \frac { f } { g } \right) ( 3 ) .$

Graph the function. - $f(x)=7 x^{2}$ $Graph the function. - f(x)=7 x^{2}$

Provide an appropriate response. -If a vertical line is drawn through the point (-5, 6), where will it intersect the x-axis?

Find the requested function value. -Find $( g \circ f ) ( - 1 )$ when $f ( x ) = \frac { x - 7 } { 8 }$ and $g ( x ) = 8 x + 1$

Graph the line and give the domain and the range. - $x+1=0$

Graph the line described. - $\text { through } ( - 2 , - 4 ) ; m = 5$ $Graph the line described. - \text { through } ( - 2 , - 4 ) ; m = 5$

Give the domain and range of the relation. - $x y = - 7$

Review of Basic Concepts

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

Filters

Exam 3: Graphs and Functions

Describe how the graph of the equation relates to the graph of y y=x2y = x ^ { 2 }y=x2 - f(x)=5x2f ( x ) = 5 x ^ { 2 }f(x)=5x2

Determine the intervals of the domain over which the function is continuous. - P(−1,−3)P(-1,-3)P(−1,−3)

Evaluate the function. -Find g(a−1)g ( a - 1 )g(a−1) when g(x)=2x+5g ( x ) = 2 x + 5g(x)=2x+5

Decide whether the relation defines a function. -

Graph the equation by plotting points. - y=x2−2y=x^{2}-2y=x2−2

Find the slope of the line satisfying the given conditions. -through (1,−7)( 1 , - 7 )(1,−7) and (−9,9)( - 9,9 )(−9,9)

Decide whether the relation defines a function. -

For the given functions f and g , find the indicated composition. - f(x)=,g(x)=8x-12 (fgg)(x)

Graph the function. - f(x)={2, if x>−5−2, if x≤−5f(x)=\left\{\begin{array}{ll}2, & \text { if } x>-5 \\-2, & \text { if } x \leq-5\end{array}\right.f(x)={2,−2,​ if x>−5 if x≤−5​

Match the description with the correct symbolic expression. -a linear function whose graph has a slope of 8

Determine whether the three points are the vertices of a right triangle. -(-5, 2), (0, 2), (0, 4)

Find the specified domain. -Use the graphs to find the value of (fg)(3)\left( \frac { f } { g } \right) ( 3 )(gf​)(3) .

Graph the function. - f(x)=7x2f(x)=7 x^{2}f(x)=7x2

Provide an appropriate response. -If a vertical line is drawn through the point (-5, 6), where will it intersect the x-axis?

Find the requested function value. -Find (g∘f)(−1)( g \circ f ) ( - 1 )(g∘f)(−1) when f(x)=x−78f ( x ) = \frac { x - 7 } { 8 }f(x)=8x−7​ and g(x)=8x+1g ( x ) = 8 x + 1g(x)=8x+1

Graph the line and give the domain and the range. - x+1=0x+1=0x+1=0

Graph the line described. - through (−2,−4);m=5\text { through } ( - 2 , - 4 ) ; m = 5 through (−2,−4);m=5

Give the domain and range of the relation. - xy=−7x y = - 7xy=−7

Review of Basic Concepts

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

Filters

Describe how the graph of the equation relates to the graph of y $y = x ^ { 2 }$ - $f ( x ) = 5 x ^ { 2 }$

Determine the intervals of the domain over which the function is continuous. - $P(-1,-3)$

Evaluate the function. -Find $g ( a - 1 )$ when $g ( x ) = 2 x + 5$

Graph the equation by plotting points. - $y=x^{2}-2$ $Graph the equation by plotting points. - y=x^{2}-2$

Find the slope of the line satisfying the given conditions. -through $( 1 , - 7 )$ and $( - 9,9 )$

Graph the function. - $f(x)=\left\{\begin{array}{ll}2, & \text { if } x>-5 \\-2, & \text { if } x \leq-5\end{array}\right.$ $Graph the function. - f(x)=\left\{\begin{array}{ll} 2, & \text { if } x>-5 \\ -2, & \text { if } x \leq-5 \end{array}\right.$

Find the specified domain. -Use the graphs to find the value of $\left( \frac { f } { g } \right) ( 3 )$ . $Find the specified domain. -Use the graphs to find the value of \left( \frac { f } { g } \right) ( 3 ) .$

Graph the function. - $f(x)=7 x^{2}$ $Graph the function. - f(x)=7 x^{2}$

Find the requested function value. -Find $( g \circ f ) ( - 1 )$ when $f ( x ) = \frac { x - 7 } { 8 }$ and $g ( x ) = 8 x + 1$

Graph the line and give the domain and the range. - $x+1=0$

Graph the line described. - $\text { through } ( - 2 , - 4 ) ; m = 5$ $Graph the line described. - \text { through } ( - 2 , - 4 ) ; m = 5$

Give the domain and range of the relation. - $x y = - 7$