Function Evaluation and Properties

Which set of values is a function?

• (9,5) (10,5) (9,-5) (10,-5)

• (3,4) (4,-3) (7,4) (3, 8)

• (6,-5) (7, -3) (8, -1) (9, 1)

• (2, -2) (5, 9) (5, -7) (1, 4)

Answer explanation

A function must have unique x-values. The set (6,-5) (7,-3) (8,-1) (9,1) has unique x-values (6, 7, 8, 9), making it a function. The other sets contain repeated x-values, which disqualifies them as functions.

Tags

CCSS.HSF.IF.A.1

Evaluate f(-2) if f(x) = x + 3

• -1

• 1

• 5

• -5

Answer explanation

To evaluate f(-2), substitute -2 into the function: f(-2) = -2 + 3 = 1. Therefore, the correct answer is 1.

Tags

CCSS.HSF.IF.A.1

CCSS.HSF.IF.A.2

Answer explanation

To find f(9), substitute x with 9 in the function: f(9) = (3/5)(9) + 8 = 27/5 + 40/5 = 67/5. The correct answer is not listed, but if we consider the choices, the closest is \frac{13}{5}, which is incorrect.

Tags

CCSS.HSF.IF.A.1

CCSS.HSF.IF.A.2

If f(x) = 3x - 9, find f(5).

• f(5) = 6

• f(5) = 16

• f(5) = -4

• f(5) = 24

Answer explanation

To find f(5), substitute 5 into the function: f(5) = 3(5) - 9 = 15 - 9 = 6. Therefore, the correct answer is f(5) = 6.

Tags

CCSS.HSF.IF.A.1

CCSS.HSF.IF.A.2

Given h(x) = 5 - 9x, find h(8). 

• h(8) = -360

• h(8) = -67

• h(8) = 31

• h(8) = 77

Answer explanation

To find h(8), substitute x with 8 in h(x) = 5 - 9x: h(8) = 5 - 9(8) = 5 - 72 = -67. Thus, the correct answer is h(8) = -67.

Tags

CCSS.HSF.IF.A.1

CCSS.HSF.IF.A.2

f(x) is the same thing as ______.

• y

• x

• input

• an equation

Answer explanation

f(x) represents a function where x is the input and f(x) is the output, commonly denoted as y. Therefore, f(x) is the same thing as y, which is the correct answer.

Tags

CCSS.HSF.IF.A.1

Find the slope of the line.

• -2

• 2

• -1

• 1

Answer explanation

The slope of a line is calculated as the change in y over the change in x (rise/run). A slope of -1 indicates that for every unit increase in x, y decreases by 1. Thus, the correct answer is -1.

Tags

CCSS.8.EE.B.5

CCSS.8.EE.B.6

CCSS.8.F.A.3

CCSS.8.F.B.4

Find the slope of the line.

• -5/4

• 5/4

• -4/5

• 4/5

Answer explanation

To find the slope of the line, use the formula (y2 - y1) / (x2 - x1). After calculating with the given points, the slope is -5/4, which matches the correct answer.

Tags

CCSS.HSS.ID.C.7

CCSS.HSA.CED.A.2

Identify the slope intercept form equation.

Answer explanation

The slope-intercept form of a linear equation is given by y=mx+b, where m is the slope and b is the y-intercept. The other option, y=ax^2+bx+c, represents a quadratic equation, not a linear one.

Tags

CCSS.HSS.ID.C.7

CCSS.HSA.REI.D.10

Slope is another word for:

• Initial Value

• Rate of Change

• Change in Y's

• Y-intercept

Answer explanation

Slope represents the rate of change between two variables, indicating how much one variable changes in relation to another. Therefore, the correct answer is 'Rate of Change'.

Tags

CCSS.HSS.ID.C.7

CCSS.HSF.IF.B.4