Question 1

Find the slope of the line passing through points $\left( \frac { 3 } { 4 } , 7 \right)$ and $\left( 7 , - \frac { 1 } { 2 } \right)$ .

Accepted Answer

A)  $- \frac { 6 } { 5 }$ 
B)  $\frac { 6 } { 5 }$ 
C)  $\frac { 26 } { 25 }$ 
D)  -$\frac { 26 } { 25 }$ 
E)  5 
A)  $- \frac { 6 } { 5 }$ 
B)  $\frac { 6 } { 5 }$ 
C)  $\frac { 26 } { 25 }$ 
D)  -$\frac { 26 } { 25 }$ 
E)  5

Question 2

A dietician is asked to design a special diet supplement using two foods. Each ounce of food X contains 31 units of calcium and each ounce of food Y contains 20 units of calcium. The minimum daily requirement in the diet is 300 units of calcium. Write a linear inequality that represents the different numbers of units of food X and food Y required.

Accepted Answer

A)  $31 X + 20 Y \geq 300$ 
B)  $20 X + 31 Y \geq 300$ 
C)  $31 X - 20 Y \geq 300$ 
D)  $31 X + 20 Y \geq 249$ 
E)  $11 X + 20 Y \geq 300$ 
A)  $31 X + 20 Y \geq 300$ 
B)  $20 X + 31 Y \geq 300$ 
C)  $31 X - 20 Y \geq 300$ 
D)  $31 X + 20 Y \geq 249$ 
E)  $11 X + 20 Y \geq 300$

Question 3

Find and simplify $f ( 4 ) + f ( 5 )$ for the function $f ( x ) = \frac { x + 2 } { x - 3 }$ .

Accepted Answer

A)  $f ( 4 ) + f ( 5 ) = 19$ 
B)  $f ( 4 ) + f ( 5 ) = \frac { 23 } { 2 }$ 
C)  $f ( 4 ) + f ( 5 ) = \frac { 23 } { 9 }$ 
D)  $f ( 4 ) + f ( 5 ) = \frac { 19 } { 2 }$ 
E)  $f ( 4 ) + f ( 5 ) = \frac { 9 } { 23 }$ 
A)  $f ( 4 ) + f ( 5 ) = 19$ 
B)  $f ( 4 ) + f ( 5 ) = \frac { 23 } { 2 }$ 
C)  $f ( 4 ) + f ( 5 ) = \frac { 23 } { 9 }$ 
D)  $f ( 4 ) + f ( 5 ) = \frac { 19 } { 2 }$ 
E)  $f ( 4 ) + f ( 5 ) = \frac { 9 } { 23 }$

Question 4

Find the domain of $f ( x ) = \sqrt { 7 - x }$ .

Accepted Answer

A) all real numbers x such that $0 \leq x \leq 7$ 
B) all real numbers x such that $x \geq 7$ 
C) all real numbers x such that $x \leq 7$ 
D) all real numbers x such that $- 7 \leq x \leq 0$ 
E) all real numbers x such that $- 7 \leq x \leq 7$ 
A) all real numbers x such that $0 \leq x \leq 7$ 
B) all real numbers x such that $x \geq 7$ 
C) all real numbers x such that $x \leq 7$ 
D) all real numbers x such that $- 7 \leq x \leq 0$ 
E) all real numbers x such that $- 7 \leq x \leq 7$

Question 5

State the slope and a point on the graph for the point-slope equation $y - 7 = 6 ( x - 8 )$ .

Accepted Answer

A)  6 ; $( - 8 , - 7 )$ 
B)  6 ; $( 8,7 )$ 
C)  7 ; $( - 8 , - 7 )$ 
D)  $7$ ; $( - 48 , - 7 )$ 
E)  $6$ ; $( 7,6 )$ 
A)  6 ; $( - 8 , - 7 )$ 
B)  6 ; $( 8,7 )$ 
C)  7 ; $( - 8 , - 7 )$ 
D)  $7$ ; $( - 48 , - 7 )$ 
E)  $6$ ; $( 7,6 )$

Question 6

State if the line passing through the points $( - 8 , - 9 )$ and $( - 2,6 )$ rises, falls, is horizontal, or is vertical.

Accepted Answer

A) The line passing through the points $( - 8 , - 9 )$ and $( - 2,6 )$ vertical. 
B) The line passing through the points $( - 8 , - 9 )$ and $( - 2,6 )$ horizontal. 
C) The line passing through the points $( - 8 , - 9 )$ and $( - 2,6 )$ rises. 
D) The line passing through the points $( - 8 , - 9 )$ and $( - 2,6 )$ falls. 
A) The line passing through the points $( - 8 , - 9 )$ and $( - 2,6 )$ vertical. 
B) The line passing through the points $( - 8 , - 9 )$ and $( - 2,6 )$ horizontal. 
C) The line passing through the points $( - 8 , - 9 )$ and $( - 2,6 )$ rises. 
D) The line passing through the points $( - 8 , - 9 )$ and $( - 2,6 )$ falls.

Question 7

An electronically controlled thermostat in a home is programmed to lower the temperature automatically during the night. The temperature T, in degrees Fahrenheit, is given in terms of t, the time on a 24 hour clock, as shown in the figure. The thermostat is then reprogrammed to produce a temperature H where $H ( t ) = T ( t - 1 )$ . Explain how this changes the temperature of the house.

Accepted Answer

A) lowers the temperature of the house 1 hour later at night, and warms up the temperature of the house 1 hour later in the morning 
B) lowers the temperature of the house 1 hour later at night, and warms up the temperature of the house 1 hour earlier in the morning 
C) lowers the temperature of the house 1 hour earlier in the morning , and warms up the temperature of the house 1 hour later in the morning 
D) lowers the temperature of the house during the day and at night 1 degree 
E) lowers the temperature of the house 1 hour earlier in the morning , and warms up the temperature of the house 1 hour earlier in the morning 
A) lowers the temperature of the house 1 hour later at night, and warms up the temperature of the house 1 hour later in the morning 
B) lowers the temperature of the house 1 hour later at night, and warms up the temperature of the house 1 hour earlier in the morning 
C) lowers the temperature of the house 1 hour earlier in the morning , and warms up the temperature of the house 1 hour later in the morning 
D) lowers the temperature of the house during the day and at night 1 degree 
E) lowers the temperature of the house 1 hour earlier in the morning , and warms up the temperature of the house 1 hour earlier in the morning

Question 8

Write the equation of the line that passes through the point $\left( 0 , - \frac { 7 } { 9 } \right)$ and has slope $m = - \frac { 9 } { 4 }$ . Write the equation in general form.

Accepted Answer

A)  $81 x - 36 y + 28 = 0$ 
B)  $81 x + 36 y + 28 = 0$ 
C)  $81 x + 36 y + 7 = 0$ 
D)  $36 x + 81 y - 28 = 0$ 
E)  $36 x + 81 y - 7 = 0$ 
A)  $81 x - 36 y + 28 = 0$ 
B)  $81 x + 36 y + 28 = 0$ 
C)  $81 x + 36 y + 7 = 0$ 
D)  $36 x + 81 y - 28 = 0$ 
E)  $36 x + 81 y - 7 = 0$

Question 9

Find the coordinates of the point located 2 units to the left of the y -axis and 9 units above the x -axis.

Accepted Answer

A)  $( 2 , - 9 )$ 
B)  $( - 2 , - 9 )$ 
C)  $( - 9,2 )$ 
D)  $( - 2,9 )$ 
E)  $( 2,9 )$ 
A)  $( 2 , - 9 )$ 
B)  $( - 2 , - 9 )$ 
C)  $( - 9,2 )$ 
D)  $( - 2,9 )$ 
E)  $( 2,9 )$

Question 10

Determine whether the lines $L _ { 1 } : y = - \frac { 1 } { 2 } x - 3$ and $L _ { 2 } : y = - \frac { 1 } { 2 } x + 4$ are parallel, perpendicular, or neither.

Accepted Answer

A) neither 
B) parallel 
C) perpendicular 
A) neither 
B) parallel 
C) perpendicular

Question 11

Find the x- and y- intercepts, if any, of $y = | x - 3 | - 7$ .

Accepted Answer

A) x- intercept at $\pm 7$ , y- intercept at -7 
B) x- intercept at -7 , y- intercept at -7 
C) x- intercept at 10 , -4 , y- intercept at -4 
D) x- intercept at $\pm 3$ , y- intercept at $7$ 
E) no intercepts 
A) x- intercept at $\pm 7$ , y- intercept at -7 
B) x- intercept at -7 , y- intercept at -7 
C) x- intercept at 10 , -4 , y- intercept at -4 
D) x- intercept at $\pm 3$ , y- intercept at $7$ 
E) no intercepts

Question 12

Write $x - 0.25 y - 2 = 0$ in slope-intercept form.

Accepted Answer

A)  $y = 4 x - 2$ 
B)  $y = - 4 x - 8$ 
C)  $y = - 4 x + 8$ 
D)  $y = - 0.25 x - 2$ 
E)  $y = 4 x - 8$ 
A)  $y = 4 x - 2$ 
B)  $y = - 4 x - 8$ 
C)  $y = - 4 x + 8$ 
D)  $y = - 0.25 x - 2$ 
E)  $y = 4 x - 8$

Question 13

Plot the points $( 1,4 ) , ( 2,0 ) , ( 5,5 )$ and connect them with line segments to form a figure.

Accepted Answer

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

Question 14

Sketch the graph of $h ( x ) = | x | - 5$ using transformations of $f ( x ) = | x |$ .

Accepted Answer

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

Question 15

Determine the domain and range of the graph of the function $C ( x ) = \sqrt { x } + 2$ .

Accepted Answer

A) The domain is all real numbers x such that $x \geq 0$ . The range is all real numbers y such that $y \geq - 2$ . 
B) The domain is all real numbers x such that $x \geq 2$ . The range is all real numbers y such that $y \geq 2$ . 
C) The domain is all real numbers x such that $x \leq 0$ . The range is all real numbers y such that $y \geq 2$ . 
D) The domain is all real numbers x such that $x \geq 2$ . The range is all real numbers y such that $y \geq 0$ . 
E) The domain is all real numbers x such that $x \geq 0$ . The range is all real numbers y such that $y \geq 2$ . 
A) The domain is all real numbers x such that $x \geq 0$ . The range is all real numbers y such that $y \geq - 2$ . 
B) The domain is all real numbers x such that $x \geq 2$ . The range is all real numbers y such that $y \geq 2$ . 
C) The domain is all real numbers x such that $x \leq 0$ . The range is all real numbers y such that $y \geq 2$ . 
D) The domain is all real numbers x such that $x \geq 2$ . The range is all real numbers y such that $y \geq 0$ . 
E) The domain is all real numbers x such that $x \geq 0$ . The range is all real numbers y such that $y \geq 2$ .

Question 16

Plot the points $( 0,0 ) , ( 0 , - 3 ) , ( 2 , - 1 )$ and $( 2 , - 4 )$ . Find the parallelogram that is obtained by connecting the points with line segments.

Accepted Answer

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

Question 17

Evaluate and simplify $f ( x ) = 12 x - 7$ at x=7 .

Accepted Answer

A)  f(7)=35 
B)  f(7)=84 
C)  f(7)=91 
D)  f(7)=77 
E)  f(7)=12 
A)  f(7)=35 
B)  f(7)=84 
C)  f(7)=91 
D)  f(7)=77 
E)  f(7)=12

Question 18

Determine if the point (-4,-3) is a solution to $x + y < 3$ .

Accepted Answer

A)  (-4,-3) is a solution 
B)  (-4,-3)  is not a solution 
A)  (-4,-3) is a solution 
B)  (-4,-3)  is not a solution

Question 19

A business purchases a van for $\$ 27,600$ . After 5 years, its depreciated value will be $\$ 12,400$ . Assuming straight line depreciation, what will be the value of the van in $4$ years?

Accepted Answer

A) $ $5,520$ 
B) $ $24,560$ 
C) $ $12,160$ 
D) $ $23,800$ 
E) $ $15,440$ 
A) $ $5,520$ 
B) $ $24,560$ 
C) $ $12,160$ 
D) $ $23,800$ 
E) $ $15,440$

Question 20

Estimate the slope of the line from the graph given below.

Accepted Answer

A) -3 
B) -2 
C)  $\frac { 1 } { 3 }$ 
D)  -$\frac { 1 } { 3 }$ 
E) 2 
A) -3 
B) -2 
C)  $\frac { 1 } { 3 }$ 
D)  -$\frac { 1 } { 3 }$ 
E) 2

Find the slope of the line passing through points $\left( \frac { 3 } { 4 } , 7 \right)$ and $\left( 7 , - \frac { 1 } { 2 } \right)$ .

Find and simplify $f ( 4 ) + f ( 5 )$ for the function $f ( x ) = \frac { x + 2 } { x - 3 }$ .

Find the domain of $f ( x ) = \sqrt { 7 - x }$ .

State the slope and a point on the graph for the point-slope equation $y - 7 = 6 ( x - 8 )$ .

State if the line passing through the points $( - 8 , - 9 )$ and $( - 2,6 )$ rises, falls, is horizontal, or is vertical.

Write the equation of the line that passes through the point $\left( 0 , - \frac { 7 } { 9 } \right)$ and has slope $m = - \frac { 9 } { 4 }$ . Write the equation in general form.

Find the coordinates of the point located 2 units to the left of the y -axis and 9 units above the x -axis.

Determine whether the lines $L _ { 1 } : y = - \frac { 1 } { 2 } x - 3$ and $L _ { 2 } : y = - \frac { 1 } { 2 } x + 4$ are parallel, perpendicular, or neither.

Find the x- and y- intercepts, if any, of $y = | x - 3 | - 7$ .

Write $x - 0.25 y - 2 = 0$ in slope-intercept form.

Plot the points $( 1,4 ) , ( 2,0 ) , ( 5,5 )$ and connect them with line segments to form a figure.

Sketch the graph of $h ( x ) = | x | - 5$ using transformations of $f ( x ) = | x |$ .

Determine the domain and range of the graph of the function $C ( x ) = \sqrt { x } + 2$ . $Determine the domain and range of the graph of the function C ( x ) = \sqrt { x } + 2 .$

Plot the points $( 0,0 ) , ( 0 , - 3 ) , ( 2 , - 1 )$ and $( 2 , - 4 )$ . Find the parallelogram that is obtained by connecting the points with line segments.

Evaluate and simplify $f ( x ) = 12 x - 7$ at x=7 .

Determine if the point (-4,-3) is a solution to $x + y < 3$ .

A business purchases a van for $\$ 27,600$ . After 5 years, its depreciated value will be $\$ 12,400$ . Assuming straight line depreciation, what will be the value of the van in $4$ years?

Estimate the slope of the line from the graph given below.

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 the slope of the line passing through points (34,7)\left( \frac { 3 } { 4 } , 7 \right)(43​,7) and (7,−12)\left( 7 , - \frac { 1 } { 2 } \right)(7,−21​) .

Find and simplify f(4)+f(5)f ( 4 ) + f ( 5 )f(4)+f(5) for the function f(x)=x+2x−3f ( x ) = \frac { x + 2 } { x - 3 }f(x)=x−3x+2​ .

Find the domain of f(x)=7−xf ( x ) = \sqrt { 7 - x }f(x)=7−x​ .

State the slope and a point on the graph for the point-slope equation y−7=6(x−8)y - 7 = 6 ( x - 8 )y−7=6(x−8) .

State if the line passing through the points (−8,−9)( - 8 , - 9 )(−8,−9) and (−2,6)( - 2,6 )(−2,6) rises, falls, is horizontal, or is vertical.

Write the equation of the line that passes through the point (0,−79)\left( 0 , - \frac { 7 } { 9 } \right)(0,−97​) and has slope m=−94m = - \frac { 9 } { 4 }m=−49​ . Write the equation in general form.

Find the coordinates of the point located 2 units to the left of the y -axis and 9 units above the x -axis.

Determine whether the lines L1:y=−12x−3L _ { 1 } : y = - \frac { 1 } { 2 } x - 3L1​:y=−21​x−3 and L2:y=−12x+4L _ { 2 } : y = - \frac { 1 } { 2 } x + 4L2​:y=−21​x+4 are parallel, perpendicular, or neither.

Find the x- and y- intercepts, if any, of y=∣x−3∣−7y = | x - 3 | - 7y=∣x−3∣−7 .

Write x−0.25y−2=0x - 0.25 y - 2 = 0x−0.25y−2=0 in slope-intercept form.

Plot the points (1,4),(2,0),(5,5)( 1,4 ) , ( 2,0 ) , ( 5,5 )(1,4),(2,0),(5,5) and connect them with line segments to form a figure.

Sketch the graph of h(x)=∣x∣−5h ( x ) = | x | - 5h(x)=∣x∣−5 using transformations of f(x)=∣x∣f ( x ) = | x |f(x)=∣x∣ .

Determine the domain and range of the graph of the function C(x)=x+2C ( x ) = \sqrt { x } + 2C(x)=x​+2 .

Plot the points (0,0),(0,−3),(2,−1)( 0,0 ) , ( 0 , - 3 ) , ( 2 , - 1 )(0,0),(0,−3),(2,−1) and (2,−4)( 2 , - 4 )(2,−4) . Find the parallelogram that is obtained by connecting the points with line segments.

Evaluate and simplify f(x)=12x−7f ( x ) = 12 x - 7f(x)=12x−7 at x=7 .

Determine if the point (-4,-3) is a solution to x+y<3x + y < 3x+y<3 .

A business purchases a van for $27,600\$ 27,600$27,600 . After 5 years, its depreciated value will be $12,400\$ 12,400$12,400 . Assuming straight line depreciation, what will be the value of the van in 444 years?

Estimate the slope of the line from the graph given below.

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 the slope of the line passing through points $\left( \frac { 3 } { 4 } , 7 \right)$ and $\left( 7 , - \frac { 1 } { 2 } \right)$ .

Find and simplify $f ( 4 ) + f ( 5 )$ for the function $f ( x ) = \frac { x + 2 } { x - 3 }$ .

Find the domain of $f ( x ) = \sqrt { 7 - x }$ .

State the slope and a point on the graph for the point-slope equation $y - 7 = 6 ( x - 8 )$ .

State if the line passing through the points $( - 8 , - 9 )$ and $( - 2,6 )$ rises, falls, is horizontal, or is vertical.

Write the equation of the line that passes through the point $\left( 0 , - \frac { 7 } { 9 } \right)$ and has slope $m = - \frac { 9 } { 4 }$ . Write the equation in general form.

Determine whether the lines $L _ { 1 } : y = - \frac { 1 } { 2 } x - 3$ and $L _ { 2 } : y = - \frac { 1 } { 2 } x + 4$ are parallel, perpendicular, or neither.

Find the x- and y- intercepts, if any, of $y = | x - 3 | - 7$ .

Write $x - 0.25 y - 2 = 0$ in slope-intercept form.

Plot the points $( 1,4 ) , ( 2,0 ) , ( 5,5 )$ and connect them with line segments to form a figure.

Sketch the graph of $h ( x ) = | x | - 5$ using transformations of $f ( x ) = | x |$ .

Determine the domain and range of the graph of the function $C ( x ) = \sqrt { x } + 2$ . $Determine the domain and range of the graph of the function C ( x ) = \sqrt { x } + 2 .$

Plot the points $( 0,0 ) , ( 0 , - 3 ) , ( 2 , - 1 )$ and $( 2 , - 4 )$ . Find the parallelogram that is obtained by connecting the points with line segments.

Evaluate and simplify $f ( x ) = 12 x - 7$ at x=7 .

Determine if the point (-4,-3) is a solution to $x + y < 3$ .

A business purchases a van for $\$ 27,600$ . After 5 years, its depreciated value will be $\$ 12,400$ . Assuming straight line depreciation, what will be the value of the van in $4$ years?