1. Determine whether the equation represents a direct variation. If so, identify the
constant of variation.
a. y
2
x
3
b. y 2 x 0 Direct variation; k
c. y 4 x
2
3
Direct variation; k
2
2 Not a direct variation
2. Determine whether the functions shown in t
1. Identify the domain of the function represented by the set of ordered pairs.
cfw_(1, 5), (4, 9), (8, 3), (11, 2)
The domain is the set of input, or x-values.
cfw_1, 4, 8, 11
2.
Determine the domain of the function represented in the table below.
x
0
3
1. Identify the x-intercept of the line whose equation is 2 x 8 y 24 .
2x 8 0
2x 0
2x
Substitute 0 for y in the equation and solve for x as follows:
2
x
2. Identify the y-intercept of the line whose equation is 5 x 20 y 100 .
5 0 20 y
20 y
Substitute 0 fo
1. Identify the independent and dependent variables in the statement below.
The number of calories you burn will depend on how many minutes you spend exercising.
The independent variable is the number of minutes, and the dependent variable is the
number o
Perform the following function operations.
1. Find f ( x) g ( x) if f ( x) = 5 x and g ( x=
) 3x 4 .
f ( x) g ( x) = 5 x(3 x 4)
= 5 x 3x 5 x 4
= 15 x 2 20 x
2. Find f ( x) g ( x) if f ( x) = 2 x 2 and g (=
x) 3x3 6 x .
f ( x) g ( x=
) 2 x 2 (3 x 3 6 x)
=
1. Identify the coordinates of points A, B, and C on the graph of the function y = f ( x)
below.
y
5
4
3
A
2
1
B
-5
-4
-3
-2
-1
1
2
3
4
5 x
-1
-2
-3
C
-4
-5
A: (-2, 3)
B: (0, 1)
C: (4, -3)
2. Identify the coordinates of points A, B, and C on the graph of
Covert the following linear equations to the requested form.
1. Rewrite the equation y 1 2( x 3) in slope-intercept form.
y
y
y
y 1
1
1
1
1
y
2( x
2 x
2x
2x
2x
3)
2 3
6
6 1
7
2. Rewrite the equation y 5
y 5
y 5
y 5
y 5 4x
4x y 5
4x y 5 5
4x y
4( x
4 x
4x
Use the distributive property to simplify each expression.
1. (17 x 2 + 5 x 6) (13 x 2 + 2 x 4)
(17 x 2 + 5 x 6) (13x 2 + 2 x 4) = 17 x 2 + 5 x 6 13 x 2 2 x + 4
= 17 x 2 13x 2 + 5 x 2 x 6 + 4
= 4 x 2 + 3x 2
2. 4(3x 2 5 x + 8)
4(3 x 2 5 x + 8) = 4 3 x 2 4
Solve the equations.
1. 4 x + 3 = 2 x 33
4 x + 3 = 2 x 33
4 x + 3 + 2 x = 2 x 33 + 2 x
6 x + 3 = 33
6 x + 3 3 = 33 3
6 x = 36
6 x 36
=
6
6
x = 6
2. m 12 = 7m + 44
m 12 = 7 m + 44
m 12 7 m = 7 m + 44 7 m
8m 12 = 44
8m 12 + 12 = 44 + 12
8m = 56
8m 56
=
8
1. Suppose y varies directly as x, and y = 16 when x = 4. Find y when x = 6.
k
y
y 16
4
x 4
4 x 4 6 24
2. Suppose y varies directly as x, and y = 5 when x = 3. Find x when y = 15.
y
k
y
x
5
3
15
3
15
5
9
5
x
3
5
x
3
3 5
x
5 3
x
3. Jennifers salary varies
Perform the following function operations.
1. Find f ( x ) + g ( x ) if f ( x ) = 12 x 5 and g ( x) = 7 x + 9 .
f ( x) + g ( x) = (12 x 5) + (7 x + 9)
= 12 x + 7 x 5 + 9
= 19 x + 4
2. Given f ( x ) = 3 x + 15 and g ( x) = 10 x , what is f (2) + g ( 3) ?
f
1. The following graph represents the conversion for temperatures measured in
degrees Fahrenheit to Celsius.
Celsius (C)
50
40
30
20
10
-50 -40 -30 -20 -10
-10
10
20
30
40 50
Fahrenheit (F)
-20
-30
-40
-50
a. What is the corresponding Celsius temperature
1. Raymond is considering adding a text message service to his cell phone plan. If it
will cost $2.50 for 10 messages and $12.50 for 50 messages, what is the rate of
change of the cost per message?
To find the rate of change, calculate the slope using the
1. Write the equation of the line with a slope of 1.2 and that passes through the
points (0, -3) in slope-intercept form.
y 1.2 x 3
The slope-intercept equation is written in the form y
b = -3.
mx b , where m = 1.2 and
2. Write the equation of the line wi
Write the equation of the line shown in each graph.
1. Write an equation in slope-intercept form to represent the line shown in the graph
below.
y
1
x 3
4
The slope-intercept equation is written in the form y mx b . The graph passes
through the y-axis at
Use the zero product property to find the value of each variable that makes the number
statement true.
1. (a 3)(b 6) = 0
Either a 3 = 0 or b 6 = 0, so
a = 3 or b = 6.
2. (x + 1)(y 2) = 0
Either x + 1 = 0 or y 2 = 0, so
x = -1 or y = 2.
3. (m 4)(n + 5) = 0
Write out the steps to solving the following equations.
1. x 4 = 2
Add 4 to both sides.
2. 3x = 9
Divide both sides by 3.
3. 3x 5 = 2
Add 5 to both sides; then divide both sides by 3.
1
x+3= 7
2
Subtract 3 from both sides; then multiply both sides by 2.
4
1. Determine whether the relation represented in the table below is a function. Explain
your answer.
x
1
3
5
7
y
4
2
4
3
The relation is a function because for each x-value, there is only one y-value.
2. Determine whether the relation represented in the t
Which identity property does each statement best represent?
1. 15 1 = 15
Identity property of multiplication
2. 17 + 0 = 17
Identity property of addition
3. Use the identity property of addition to write the number that completes each equation.
a. _ + 0 =
1. This is a graph of a function. Use the points plotted on the graph to identify three
points that the graph of the inverse passes through.
(-4, -3), (2, 0), (4, 1)
y
5
4
3
2
1
-5
-4
-3
-2
-1
1
2
4
3
5
x
-1
-2
-3
-4
-5
2. This is a graph of a function. U
1. Plot the solution to x = 4 on the number line below.
2. Plot the solution to x 2 = 5 on the number line below.
3. Write an absolute value expression to describe the distance between -5 and 4 on the
number line.
5 4 or 4 (5)
4. Simplify the expression:
Use the associative property to rewrite each expression.
1. (x + 21) + 12
= x + (21 + 12)
2. (m + n) + 2n
= m + (n + 2n)
Use the commutative and associative properties to simplify each expression.
3. (12x + 2) + 3
= 12x + (2 + 3)
= 12x + 5
4. 7 p 4
47 p
1. In what linear form is the equation y
Since the equation is in the form y
2
x 1 written?
5
mx b , it is written in slope-intercept form.
2. In what linear form is the equation 5 x y
5 written?
Since the equation is in the form ax by
c , it is written i