Mastery of Piecewise, Linear, and Quadratic Functions

Graph the piecewise function: $$ f(x) = \begin{cases} x + 2 & \text{if } x < 0 \\ x^2 & \text{if } x \geq 0 \end{cases} $$ Which of the following describes the graph?

• A straight line for all x

• A parabola for all x

• A straight line for x < 0 and a parabola for x ≥ 0

• A parabola for x < 0 and a straight line for x ≥ 0

Tags

CCSS.HSF-IF.C.7B

Which of the following equations represents a linear function?

• y = x^2 + 3x - 7

• y = 2x + 5

• y = |x| + 1

• y = 3x^2 - x + 4

Tags

CCSS.8.F.A.3

What is the vertex of the parabola represented by the equation y = 2(x - 3)^2 + 4?

• (3, 4)

• (-3, -4)

• (0, 4)

• (3, 2)

Identify the vertex of the quadratic function f(x) = x^2 - 6x + 8.

• (3, -1)

• (6, 8)

• (-3, -1)

• (3, -10)

Which of the following is a piecewise function?

• f(x) = 3x + 2

• f(x) = x^2

• f(x) = \begin{cases} 2x & \text{if } x \leq 1 \\ x^2 & \text{if } x > 1 \end{cases}

• f(x) = |x - 2|

What is the slope of the linear function represented by the equation y = -4x + 1?

• 1

• -4

• 4

• 0

Tags

CCSS.8.EE.B.5

Graph the piecewise function: $$ f(x) = \begin{cases} -x & \text{if } x \leq 2 \\ x^2 - 4 & \text{if } x > 2 \end{cases} $$ What is the value of f(2)?

• -2

• 0

• 4

• Undefined

Tags

CCSS.HSF-IF.C.7B

Which of the following is the graph of a quadratic function?

• A straight line that passes through the origin

• A U-shaped curve that opens upwards

• A V-shaped graph

• A horizontal line

Tags

CCSS.HSF-IF.C.7A

If the vertex of a parabola is at (h, k), which of the following represents the vertex form of a quadratic function?

• y = a(x - h)^2 + k

• y = ax^2 + bx + c

• y = a(x + h) + k

• y = a(hx + k)^2

Consider the piecewise function: $$ f(x) = \begin{cases} 3x - 1 & \text{if } x < 0 \\ x^2 + 2x & \text{if } x \geq 0 \end{cases} $$ What is the value of f(0)?

• -1

• 0

• 2

• Undefined

Tags

CCSS.HSF.IF.A.2