Relations and Functions Worksheet

These ordered pairs represent a relation that is not a function: {(-1, 3), (2, 3), (4, 0), (6, 3), (6, 5)} Which of the following would make the relation a function?

• Replace (6, 3) with (4, 3)

• Replace (6, 5) with (2, 6)

• Replace (6, 3) with (6, -2)

• Replace (6, 5) with (5, 6)

Answer explanation

The relation is not a function because (6, 3) and (6, 5) share the same first element (6). Replacing (6, 5) with (5, 6) introduces a new first element (5), ensuring each input has a unique output, thus making it a function.

Tags

CCSS.8.F.A.1

Simplify: 3(2x - 5y) + 7(4x + y)

• 34x - 8y

• 34x + 22y

• 34x - 4y

• 34x² - 8y²

Answer explanation

Distribute: 3(2x - 5y) = 6x - 15y and 7(4x + y) = 28x + 7y. Combine like terms: 6x + 28x = 34x and -15y + 7y = -8y. Thus, the simplified expression is 34x - 8y, which matches the correct choice.

Tags

CCSS.6.EE.A.3

• -60

• 24

• 60

• 78

Answer explanation

Substituting x = -3 into the expression 2x^2 - 14x gives 2(-3)^2 - 14(-3) = 2(9) + 42 = 18 + 42 = 60. Thus, the correct answer is 60.

Tags

CCSS.6.EE.A.2C

Write an equation in slope-intercept form for the line that passes through the point (-8, 2) and is parallel to the graph of the y = (5/4)x - 1.

• y = (5/4)x + 2

• y = (5/4)x + 12

• y = -(4/5)x + 2

• y = -(4/5)x - 4 2/5

Answer explanation

The slope of the given line is 5/4. A parallel line has the same slope. Using point-slope form with point (-8, 2), we find the y-intercept to be 12. Thus, the equation is y = (5/4)x + 12.

Simplify √112

• 4√7

• 7√16

• 16√7

• 2√28

Answer explanation

To simplify √112, we can factor it as √(16 * 7) = √16 * √7 = 4√7. Thus, the correct answer is 4√7.

Solve the equation: 2 - (3 + y) = 6

• 5

• -5

• -7

• 7

Answer explanation

To solve 2 - (3 + y) = 6, first simplify: 2 - 3 - y = 6. This gives -1 - y = 6. Adding 1 to both sides results in -y = 7. Thus, y = -7, which is the correct answer.

Tags

CCSS.6.EE.B.7

Evaluate: 24 – 3(12 – 7)²

• 525

• -51

• -261

• -201

Answer explanation

First, calculate the expression inside the parentheses: 12 - 7 = 5. Then square it: 5² = 25. Next, multiply by 3: 3 * 25 = 75. Finally, subtract from 24: 24 - 75 = -51. Thus, the correct answer is -51.

Tags

CCSS.6.EE.A.2C

Answer explanation

To simplify \( \frac{-64a^{-2}b^8}{8a^3b^{-3}} \), divide coefficients and apply the laws of exponents: \( \frac{-64}{8} = -8 \), \( a^{-2}/a^3 = a^{-5} \), and \( b^8/b^{-3} = b^{11} \). Thus, the result is \( \frac{-8b^{11}}{a^5} \).

Tags

CCSS.HSA.APR.A.1

The points on the graph represent a relation. What are the domain and range of the relation? A graph with the following points plotted: (-3, 3), (1, 1), (3, 1), (4, -2)

• Domain = {-2, 1, 3}; Range = {-3, 1, 3, 4}

• Domain = {-2, 1, 3}; Range = {-3, 1, 4}

• Domain = {-3, 1, 4}; Range = {-2, 1, 3}

• Domain = {-3, 1, 3, 4}; Range = {-2, 1, 3}

Answer explanation

The domain consists of the x-coordinates: {-3, 1, 3, 4}. The range consists of the y-coordinates: {-2, 1, 3}. Thus, the correct choice is Domain = {-3, 1, 3, 4}; Range = {-2, 1, 3}.

• 0

• 1

• x

Answer explanation

Any non-zero number raised to the power of 0 equals 1. Therefore, (x^5)^0 simplifies to 1.