Question 1

Find and simplify $f ( a + 8 )$ for the function $f ( x ) = 12 x - 7$ .

Accepted Answer

A)  $f ( a + 8 ) = 12 a + 48$ 
B)  $f ( a + 8 ) = 89$ 
C)  $f ( a + 8 ) = 12 a + 103$ 
D)  $f ( a + 8 ) = 12 a + 89$ 
E)  $f ( a + 8 ) = 12 a + 13$ 
A)  $f ( a + 8 ) = 12 a + 48$ 
B)  $f ( a + 8 ) = 89$ 
C)  $f ( a + 8 ) = 12 a + 103$ 
D)  $f ( a + 8 ) = 12 a + 89$ 
E)  $f ( a + 8 ) = 12 a + 13$

Question 2

Given $f ( x ) = 5 x + 4$ , evaluate $\frac { f ( x - 9 ) - f ( 9 ) } { x }$ .

Accepted Answer

A)  $\frac { 5 x - 90 } { x }$ 
B)  $\frac { 5 x - 72 } { x }$ 
C)  $\frac { 5 x + 90 } { x }$ 
D)  $\frac { 5 x - 10 } { x }$ 
E)  $x$ 
A)  $\frac { 5 x - 90 } { x }$ 
B)  $\frac { 5 x - 72 } { x }$ 
C)  $\frac { 5 x + 90 } { x }$ 
D)  $\frac { 5 x - 10 } { x }$ 
E)  $x$

Question 3

Sketch the graph of the equation $y = - | x | + 1$ and label three points on the graph.

Accepted Answer

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

Question 4

Evaluate and simplify $f ( x ) = \frac { x + 2 } { x - 3 }$ at x=-5 .

Accepted Answer

A)  $f ( - 5 ) = - \frac { 2 } { 7 }$ 
B)  $f ( - 5 ) = \frac { 2 } { 7 }$ 
C)  $f ( - 5 ) = \frac { 3 } { 8 }$ 
D)  $f ( - 5 ) = - \frac { 3 } { 8 }$ 
E)  $f ( - 5 ) = \frac { 7 } { 2 }$ 
A)  $f ( - 5 ) = - \frac { 2 } { 7 }$ 
B)  $f ( - 5 ) = \frac { 2 } { 7 }$ 
C)  $f ( - 5 ) = \frac { 3 } { 8 }$ 
D)  $f ( - 5 ) = - \frac { 3 } { 8 }$ 
E)  $f ( - 5 ) = \frac { 7 } { 2 }$

Question 5

Sketch the graph of the line $- 3 x + 2 y + 6 = 0$ by plotting the x - and y -intercepts.

Accepted Answer

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

Question 6

Sketch a graph of the equation $- 6 x + 7 y = 42$ . Use the Vertical Line Test to determine whether y is a function of x .

Accepted Answer

A) y is a function of x .   
B) y is not a function of x .   
C) y is a function of x .   
D) y is not a function of x .   
E) y is a function of x .   
A) y is a function of x .   
B) y is not a function of x .   
C) y is a function of x .   
D) y is not a function of x .   
E) y is a function of x .

Question 7

Find and simplify f(a)+f(6) for the function $f ( x ) = 12 x - 7$ .

Accepted Answer

A)  $f ( a ) + f ( 6 ) = 12 a + 58$ 
B)  $f ( a ) + f ( 6 ) = 12 a + 79$ 
C)  $f ( a ) + f ( 6 ) = 12 a + 36$ 
D)  $f ( a ) + f ( 6 ) = 12 a + 11$ 
E)  $f ( a ) + f ( 6 ) = 12 a + 72$ 
A)  $f ( a ) + f ( 6 ) = 12 a + 58$ 
B)  $f ( a ) + f ( 6 ) = 12 a + 79$ 
C)  $f ( a ) + f ( 6 ) = 12 a + 36$ 
D)  $f ( a ) + f ( 6 ) = 12 a + 11$ 
E)  $f ( a ) + f ( 6 ) = 12 a + 72$

Question 8

The slope, or pitch, of a roof is such that is rises (or falls)6 feet for every 5 feet of horizontal distance. Determine the maximum height of the attic for a 30-foot wide house. Round your answer to two decimal places.

Accepted Answer

A) 36.00 feet 
B) 12.50 feet 
C) 15.00 feet 
D) 19.20 feet 
E) 18.00 feet 
A) 36.00 feet 
B) 12.50 feet 
C) 15.00 feet 
D) 19.20 feet 
E) 18.00 feet

Question 9

Evaluate and simplify $f ( x ) = \frac { x } { x + 2 }$ at x=4 .

Accepted Answer

A)  $f ( 4 ) = - \frac { 2 } { 3 }$ 
B)  $f ( 4 ) = \frac { 1 } { 3 }$ 
C)  $f ( 4 ) = \frac { 2 } { 3 }$ 
D)  $f ( 4 ) = \frac { 3 } { 2 }$ 
E)  $f ( 4 ) = - \frac { 3 } { 2 }$ 
A)  $f ( 4 ) = - \frac { 2 } { 3 }$ 
B)  $f ( 4 ) = \frac { 1 } { 3 }$ 
C)  $f ( 4 ) = \frac { 2 } { 3 }$ 
D)  $f ( 4 ) = \frac { 3 } { 2 }$ 
E)  $f ( 4 ) = - \frac { 3 } { 2 }$

Question 10

Use a graphing calculator to aid in sketching the graph of the linear inequality $5 x + 8 y + 11 \leq 0$ .

Accepted Answer

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

Question 11

Determine all possible quadrants in which the point can be located. Assume $y \neq 0$ . $( - 3 , y )$ y is a real number

Accepted Answer

A) Quadrants I and II 
B) Quadrants III and IV 
C) Quadrants IV and I 
D) Quadrants II and III 
E) Quadrants II and IV 
A) Quadrants I and II 
B) Quadrants III and IV 
C) Quadrants IV and I 
D) Quadrants II and III 
E) Quadrants II and IV

Question 12

Determine the quadrant in which the point is located without plotting the point. $\left( \frac { 19 } { 10 } , - \frac { 5 } { 6 } \right)$

Accepted Answer

A) Quadrant III 
B) Quadrant IV 
C) Quadrant I 
D) Quadrant II 
A) Quadrant III 
B) Quadrant IV 
C) Quadrant I 
D) Quadrant II

Question 13

Write an equation of the line that passes through $\left( - 8 , \frac { 5 } { 2 } \right)$ and has a slope of $m = \frac { 1 } { 6 }$ .

Accepted Answer

A)  $- x + 6 y = - 38$ 
B)  $- x + y = - 38$ 
C)  $x + 6 y = - 41$ 
D)  $- x + 6 y = 23$ 
E)  $- x + 6 y = - 23$ 
A)  $- x + 6 y = - 38$ 
B)  $- x + y = - 38$ 
C)  $x + 6 y = - 41$ 
D)  $- x + 6 y = 23$ 
E)  $- x + 6 y = - 23$

Question 14

The point (-4,-3) is on a line with slope 3. Find two additional points on the line.

Accepted Answer

A)  (-3,0) and (-5,-6) 
B)  (-1,-2) and (-7,-4) 
C)  (-7,-4) and (-10,-4) 
D)  $( - 3 , - 6 )$ and $( - 5,0 )$ 
E)  $( - 2,3 )$ and $( - 5 , - 9 )$ 
A)  (-3,0) and (-5,-6) 
B)  (-1,-2) and (-7,-4) 
C)  (-7,-4) and (-10,-4) 
D)  $( - 3 , - 6 )$ and $( - 5,0 )$ 
E)  $( - 2,3 )$ and $( - 5 , - 9 )$

Question 15

Match the correct equation with the given graph.

Accepted Answer

A)  $y = 2 + x$ 
B)  $y = - 2 + x$ 
C)  $y = - 2 x$ 
D)  $y = - 2 - x$ 
E)  $y = 2 - x$ 
A)  $y = 2 + x$ 
B)  $y = - 2 + x$ 
C)  $y = - 2 x$ 
D)  $y = - 2 - x$ 
E)  $y = 2 - x$

Question 16

Sketch the graph of $f ( x ) = \left\{ \begin{array} { c c } 
x + 8 & x < 0 \
8 - 2 & x \geq 0
\end{array} \right.$ .

Accepted Answer

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

Question 17

Determine which of the points is a solution of the inequality $4 x + 5 y \leq - 58$ .

Accepted Answer

A)  (10,4) 
B)  (8,4) 
C)  (3,-4) 
D)  (-10,-4) 
E)  (-3,-1) 
A)  (10,4) 
B)  (8,4) 
C)  (3,-4) 
D)  (-10,-4) 
E)  (-3,-1)

Question 18

Sketch the graph of $y = - x ( x + 4 )$ .

Accepted Answer

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

Question 19

Find the perimeter of the triangle with the vertices $( - 4,0 ) , ( 0,8 )$ and $( 1,0 )$ . Round your answer to two decimal places.

Accepted Answer

A)  17.71 
B)  22.01 
C)  24.71 
D)  18.01 
E)  19.71 
A)  17.71 
B)  22.01 
C)  24.71 
D)  18.01 
E)  19.71

Question 20

Sketch the graph of the linear inequality $x + y < 0$.

Accepted Answer

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

Find and simplify $f ( a + 8 )$ for the function $f ( x ) = 12 x - 7$ .

Given $f ( x ) = 5 x + 4$ , evaluate $\frac { f ( x - 9 ) - f ( 9 ) } { x }$ .

Sketch the graph of the equation $y = - | x | + 1$ and label three points on the graph.

Evaluate and simplify $f ( x ) = \frac { x + 2 } { x - 3 }$ at x=-5 .

Sketch the graph of the line $- 3 x + 2 y + 6 = 0$ by plotting the x - and y -intercepts.

Sketch a graph of the equation $- 6 x + 7 y = 42$ . Use the Vertical Line Test to determine whether y is a function of x .

Find and simplify f(a)+f(6) for the function $f ( x ) = 12 x - 7$ .

The slope, or pitch, of a roof is such that is rises (or falls)6 feet for every 5 feet of horizontal distance. Determine the maximum height of the attic for a 30-foot wide house. Round your answer to two decimal places.

Evaluate and simplify $f ( x ) = \frac { x } { x + 2 }$ at x=4 .

Use a graphing calculator to aid in sketching the graph of the linear inequality $5 x + 8 y + 11 \leq 0$ .

Determine all possible quadrants in which the point can be located. Assume $y \neq 0$ . $( - 3 , y )$ y is a real number

Determine the quadrant in which the point is located without plotting the point. $\left( \frac { 19 } { 10 } , - \frac { 5 } { 6 } \right)$

Write an equation of the line that passes through $\left( - 8 , \frac { 5 } { 2 } \right)$ and has a slope of $m = \frac { 1 } { 6 }$ .

The point (-4,-3) is on a line with slope 3. Find two additional points on the line.

Match the correct equation with the given graph.

Sketch the graph of $f ( x ) = \left\{ \begin{array} { c c } x + 8 & x < 0 \\8 - 2 & x \geq 0\end{array} \right.$ .

Determine which of the points is a solution of the inequality $4 x + 5 y \leq - 58$ .

Sketch the graph of $y = - x ( x + 4 )$ .

Find the perimeter of the triangle with the vertices $( - 4,0 ) , ( 0,8 )$ and $( 1,0 )$ . Round your answer to two decimal places.

Sketch the graph of the linear inequality $x + y < 0$ .

Fundamentals of Algebra

Linear Equations and Inequalities

Systems of Equations and Inequalities

Polynomials and Factoring

Rational Expressions, Equations, and Functions

Radicals and Complex Numbers

Quadratic Equations, Functions, and Inequalities

Exponential and Logarithmic Functions

Conics

Sequences, Series, and the Binomial Theorem

Filters

Exam 3: Graphs and Functions

Find and simplify f(a+8)f ( a + 8 )f(a+8) for the function f(x)=12x−7f ( x ) = 12 x - 7f(x)=12x−7 .

Given f(x)=5x+4f ( x ) = 5 x + 4f(x)=5x+4 , evaluate f(x−9)−f(9)x\frac { f ( x - 9 ) - f ( 9 ) } { x }xf(x−9)−f(9)​ .

Sketch the graph of the equation y=−∣x∣+1y = - | x | + 1y=−∣x∣+1 and label three points on the graph.

Evaluate and simplify f(x)=x+2x−3f ( x ) = \frac { x + 2 } { x - 3 }f(x)=x−3x+2​ at x=-5 .

Sketch the graph of the line −3x+2y+6=0- 3 x + 2 y + 6 = 0−3x+2y+6=0 by plotting the x - and y -intercepts.

Sketch a graph of the equation −6x+7y=42- 6 x + 7 y = 42−6x+7y=42 . Use the Vertical Line Test to determine whether y is a function of x .

Find and simplify f(a)+f(6) for the function f(x)=12x−7f ( x ) = 12 x - 7f(x)=12x−7 .

The slope, or pitch, of a roof is such that is rises (or falls)6 feet for every 5 feet of horizontal distance. Determine the maximum height of the attic for a 30-foot wide house. Round your answer to two decimal places.

Evaluate and simplify f(x)=xx+2f ( x ) = \frac { x } { x + 2 }f(x)=x+2x​ at x=4 .

Use a graphing calculator to aid in sketching the graph of the linear inequality 5x+8y+11≤05 x + 8 y + 11 \leq 05x+8y+11≤0 .

Determine all possible quadrants in which the point can be located. Assume y≠0y \neq 0y=0 . (−3,y)( - 3 , y )(−3,y) y is a real number

Determine the quadrant in which the point is located without plotting the point. (1910,−56)\left( \frac { 19 } { 10 } , - \frac { 5 } { 6 } \right)(1019​,−65​)

Write an equation of the line that passes through (−8,52)\left( - 8 , \frac { 5 } { 2 } \right)(−8,25​) and has a slope of m=16m = \frac { 1 } { 6 }m=61​ .

The point (-4,-3) is on a line with slope 3. Find two additional points on the line.

Match the correct equation with the given graph.

Sketch the graph of f(x)={x+8x<08−2x≥0f ( x ) = \left\{ \begin{array} { c c } x + 8 & x < 0 \\8 - 2 & x \geq 0\end{array} \right.f(x)={x+88−2​x<0x≥0​ .

Determine which of the points is a solution of the inequality 4x+5y≤−584 x + 5 y \leq - 584x+5y≤−58 .

Sketch the graph of y=−x(x+4)y = - x ( x + 4 )y=−x(x+4) .

Find the perimeter of the triangle with the vertices (−4,0),(0,8)( - 4,0 ) , ( 0,8 )(−4,0),(0,8) and (1,0)( 1,0 )(1,0) . Round your answer to two decimal places.

Sketch the graph of the linear inequality x+y<0x + y < 0x+y<0 .

Fundamentals of Algebra

Linear Equations and Inequalities

Systems of Equations and Inequalities

Polynomials and Factoring

Rational Expressions, Equations, and Functions

Radicals and Complex Numbers

Quadratic Equations, Functions, and Inequalities

Exponential and Logarithmic Functions

Conics

Sequences, Series, and the Binomial Theorem

Filters

Find and simplify $f ( a + 8 )$ for the function $f ( x ) = 12 x - 7$ .

Given $f ( x ) = 5 x + 4$ , evaluate $\frac { f ( x - 9 ) - f ( 9 ) } { x }$ .

Sketch the graph of the equation $y = - | x | + 1$ and label three points on the graph.

Evaluate and simplify $f ( x ) = \frac { x + 2 } { x - 3 }$ at x=-5 .

Sketch the graph of the line $- 3 x + 2 y + 6 = 0$ by plotting the x - and y -intercepts.

Sketch a graph of the equation $- 6 x + 7 y = 42$ . Use the Vertical Line Test to determine whether y is a function of x .

Find and simplify f(a)+f(6) for the function $f ( x ) = 12 x - 7$ .

Evaluate and simplify $f ( x ) = \frac { x } { x + 2 }$ at x=4 .

Use a graphing calculator to aid in sketching the graph of the linear inequality $5 x + 8 y + 11 \leq 0$ .

Determine all possible quadrants in which the point can be located. Assume $y \neq 0$ . $( - 3 , y )$ y is a real number

Determine the quadrant in which the point is located without plotting the point. $\left( \frac { 19 } { 10 } , - \frac { 5 } { 6 } \right)$

Write an equation of the line that passes through $\left( - 8 , \frac { 5 } { 2 } \right)$ and has a slope of $m = \frac { 1 } { 6 }$ .

Sketch the graph of $f ( x ) = \left\{ \begin{array} { c c } x + 8 & x < 0 \\8 - 2 & x \geq 0\end{array} \right.$ .

Determine which of the points is a solution of the inequality $4 x + 5 y \leq - 58$ .

Sketch the graph of $y = - x ( x + 4 )$ .

Find the perimeter of the triangle with the vertices $( - 4,0 ) , ( 0,8 )$ and $( 1,0 )$ . Round your answer to two decimal places.

Sketch the graph of the linear inequality $x + y < 0$ .