5-1 The Absolute Value Functions

Which of the following statement(s) describes the rate of change of f over the interval 1.5 ≤ x ≤ 3? Select all that apply.

• The rate of change is 1/2.

• The rate of change is 2.

• The rate of change is constant.

• The rate of change is increasing

• The rate of change is does not exist

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6

The range of f(x) = |x| is y ≥ 0. If a < 0 for g(x) = a|x|, what is the range of function g?

Mathematical Equivalence

ON

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. What is his walking speed?

• 280 ft/min

• 260 ft/min

• 250 ft/min

• 270 ft/min

Tags

CCSS.HSF.IF.B.4

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

• 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

How does changing the sign of the constant a from positive to negative affect the domain and range of

f(x)=a|x|​?

• The domain remains all real numbers. The range changes from y≥0 to y≤0.

• The domain remains all real numbers. The range changes from y≤0 to y≥0.

• The domain changes from positive real numbers to negative real numbers. The range remains

  y≥0.

• 
  The domain changes from negative real numbers to positive real numbers. The range remains

  y≤0.

Compare and contrast the graph of f(x)=x and the graph of f(x)=x. How are the two graphs​ alike? Select all that apply.

• Both have the same values when

  x≥0.

• Both have range of all positive real numbers.

• Both have a domain of all real numbers.

• Both have the same values when x≤0.

• Both have an​ x-intercept and​ y-intercept at the origin.

Sketch the graph of the function. Label the vertex of the​ V-shape.

​f(x)=6|x|

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Graph the function using transformations.

​g(x)=-2|x|

Each grid shows ​f(x)=x in blue. Which grid also​ shows, in pink​, ​g(x)=−2x​?

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The graph on the right shows the remaining life​ expectancy, E, in years for females of age x. The average rate of change of life expectancy between the ages of 50 and 60 is _____.

​(Round decimal answers to the nearest hundredth.)

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6

Write an equation of the absolute value function graph. ​(Simplify your answer. Use integers or fractions for any numbers in the​ expression.)

y=?

Tags

CCSS.HSF-IF.C.7D