Expressions, Equations & Functions

Order of Operations

100

7 + 2(9-3)

19

200

[(2^5 - 5) ÷ 9]11

33

300

Evaluate each expression if a=4 and c=9. c + 3a

21

400

Evaluate each expression if a=4, b=3 and c=9. (a^2 + 2bc) ÷ 7

10

500

One-scoop sundae is $2.75 and two-scoop sundae is $4.25. Find the total cost of a 3 one-scoop sundaes and 2 two-scoop sundaes.

$16.75

Properties

100

Evaluate and name the properties used. 8 x 0.5 x 5

8 x 0.5 x 5 = (8 x 5) x 0.5 Commutative/Associative = 40 x 0.5 Substitution = 20 Substitution

200

Evaluate and name the properties used. (16 - 4^2) + 9

(16 - 4^2) + 9 = 16 - 16 + 9 Substitution = 0 + 9 Additive Inverse = 9 Additive Identity

300

Evaluate and name the properties used. 18 x 3(1 ÷ 3)

18 x 3(1 ÷ 3) = 18 x 3(1/3) Substitution = 18 x 1 Multiplicative Inverse = 18 Multiplicative Identity

400

Use the Distributive Property to solve. -2(5-3)

-2(5) - (-2)(3) -10 - (-6) -10 + 6 -4

500

Rewrite using the Distributive Property and simplify. -4(5 - 2t)

-4(5 - 2t) = -4(5) - (-4)(2t) = -20 - (-8t) = -20 + 8t

Equations

100

Solve the equation. a = 24 - 7(3)

3

200

Find the solution set if the replacement set is y:{6,8,10,12,14} y - 9 = 3

12

300

Find the solution set if the replacement set is y:{6,8,10,12,14} 4y = 32

8

400

Find the solution set if the replacement set is y:{6,8,10,12,14} 42/y = 7

6

500

Shandra's age is four more than three times Sherita's age. Write an equation for Shandra's age. Solve if Sherita is 3 years old.

3K + 4 = E If Sherita is 3, then Shandra is 13

Relations & Functions

100

Determine the domain and range. {(-1,1), (0,-2), (3,1), (4,-1)}

Domain Range 0 -2 -1 -1 3 1 4

200

If f(x) = 2x + 4, what is f(0).

f(0) = 2x + 4 = 2(0) + 4 = 0 + 4 = 4

300

If f(x) = 2x + 4, what is f(-3).

f(-3) = 2x + 4 = 2(-3) + 4 = -6 + 4 = -2

400

On average, 7 plants grow for every 10 seeds of a certain type planted. Make a table to determine the domain and range to show the relationship between seeds planted and plants growing for 50, 100, 150 and 200 seeds.

Domain Range 50 35 100 70 150 105 200 140

500

If f(x) = 2x + 4, what is f(m + 2).

f(m + 2) = 2(m + 2) + 4 = 2m + 4 + 4 = 2m + 8

Interpreting Graphs

100

Explain the difference between the y-intercept and x-intercept.

y-intercept: where the graph intersects the y-axis (x-coordinate is 0) x-intercept: where the graph intersects the x-axis (y-coordinate is 0)

200

Fill in the blanks. A function is _____where its graph lies above the x-axis, and _____ where its graphs lies below the x-axis. When viewed from left to right, a function is _____ where the graph goes up and _____ where the graph goes down.

A function is POSITIVE where its graph lies above the x-axis, and NEGATIVE where its graphs lies below the x-axis. When viewed from left to right, a function is INCREASING where the graph goes up and DECREASING where the graph goes down.

300

Explain the difference between the extrema, relative minimum and relative maximum.

Relative minimum - on a graph where there is no nearby points with a lesser y-coordinate Relative maximum - on a graph where there is no nearby points with a greater y-coordinate

400

True or False. Explain. Functions have at most one y-intercept.

True, a function can have no more than one y-intercept. If a graph has more than one y-intercept then it is not a graph of a function.

500

What is the purpose of the Vertical Line Test and how can it be used? What is the difference between a continuous function and discrete function.

Vertical Line Test - used to see if a graph represents a function Continuous Function - a function graphed with a line or smooth curve Discrete Function - a graph that consists of points that are not connected