Topic 5 - Piecewise Functions

Select all the statements that are true of the function shown in the graph.

• The function is increasing over the interval 0 ≤ x ≤ 3 .

• The function is decreasing over the interval 0 ≤ x ≤ 3 .

• The function is increasing over the interval 1 ≤ x ≤ 3 .

• The function is increasing over the interval 0 ≤ x ≤ 1 .

• The function is decreasing over the interval 0 ≤ x ≤ 1 .

Timothy walks from home to a mailbox. After walking 15 min, he puts a letter in the mailbox. Then he walks home at the same speed. The graph shows his distance from the mailbox as a function of time. Select all the statements that are true of the function.

• The x -intercept is (0, 3,750) .

• The x -intercept is (15, 0) .

• The y -intercept is (0, 3,750) .

• The y -intercept is (15, 0) .

• The y -intercepts are (0, 3,750) and (30, 3,750) .

Tags

CCSS.HSF.IF.B.4

What are the domain and range of h(x) = 3 |x| ?

• domain: all real numbers; range: y ≤ 0

• domain: x ≥ 0 ; range: all real numbers

• domain: x ≤ 0 ; range: all real numbers

• domain: all real numbers; range: y ≥ 0

• 3x
• -3x
• x
• -x

Using the graph shown, over what part of the domain is the function decreasing?

Using the graph shown, over what part of the domain is the function increasing?

Which rule defines the function in the graph?

Tags

CCSS.HSF-IF.C.7B

Which point is included in the graph of the ceiling function f(x) = ⌈ x ⌉ ?

• (−0.5, −1)

• (−1.5, −2)

• (−3.5, −3)

• (−3.5, −4)

Tags

CCSS.HSF-IF.C.7B

Evaluate the floor functions for the given value. Are the two values the same?

f(x) = 2 ⌊ x ⌋ ; g(x) = ⌊ 2x ⌋ ; x = 1.2

• yes; f(1.2) = 2 = g(1.2)

• yes; f(1.2) = 2.4 = g(1.2)

• no; f(1.2) = 2 , g(1.2) = 3

• no; f(1.2) = 3 , g(1.2) = 2

Tags

CCSS.HSF.IF.A.2