Understanding Functions and Their Graphs

Which of the following graphs represents a function?

• A vertical line

• A horizontal line

• A circle

• A parabola opening upwards

Answer explanation

A function must pass the vertical line test, meaning each input has only one output. A horizontal line is a function as it assigns one output for every input. A vertical line, circle, and parabola do not meet this criterion.

Tags

CCSS.HSF.IF.A.1

• 5

• 8

• 11

• 13

Answer explanation

To find the output of the function f(x) = 2x + 3 when x = 4, substitute 4 into the function: f(4) = 2(4) + 3 = 8 + 3 = 11. Therefore, the correct answer is 11.

Tags

CCSS.HSF.IF.A.1

CCSS.HSF.IF.A.2

• 2

• 4

• 6

• 8

Answer explanation

The function passes through the point (2, 4), meaning that when the input is 2, the output is 4. Therefore, the correct answer is 4.

Tags

CCSS.HSF.IF.A.1

CCSS.HSF.IF.A.2

Which of the following rules defines a function?

Answer explanation

The equation y = x^2 + 1 defines a function because for each x, there is exactly one corresponding y value. In contrast, y = ±√x and y^2 = x can yield multiple y values for a single x, and x = 3 is a vertical line, not a function.

Tags

CCSS.HSF.IF.A.1

• -11

• -1

• 1

• 11

Answer explanation

To evaluate g(x) = 3x - 5 for x = -2, substitute -2 into the function: g(-2) = 3(-2) - 5 = -6 - 5 = -11. Thus, the correct answer is -11.

Tags

CCSS.HSF.IF.A.1

CCSS.HSF.IF.A.2

a) Function or not? (a)  

b) Domain =​ (b)  

Range =​ (c)  

• Function

• Not a Function

• {-5, -2,  2}

• {-4, 1. 3}

Answer explanation

The relation is not a function because it assigns multiple outputs to at least one input. The domain is {-5, -2, 2} and the range is {-4, 1, 3}, confirming the correct choices.

Tags

CCSS.HSF.IF.A.1

CCSS.HSF.IF.A.2

Which representation does NOT show y as a function of x?

• A

• B

• C

• D

Answer explanation

Choice D does not show y as a function of x because it likely represents multiple y-values for a single x-value, violating the definition of a function. In a function, each input (x) must correspond to exactly one output (y).

Tags

CCSS.HSF.IF.A.1

CCSS.HSF.IF.A.2

CCSS.HSA.CED.A.2

CCSS.HSA.REI.D.10

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7