5
practice testMultiple Choice

Practice Test

Question 5 • Mathematics II

The graph of f of x is equal to absolute value of x is stretched by a factor of 0 point 3 and translated down 4 units. Which statement about the domain and range of each function is correct?

Answer
A
The domain of the transformed function is all real numbers and is, therefore, different from that of the parent function.
B
The domain of the transformed function and the parent function are both all real numbers.
C
The range of the transformed function is all real numbers greater than or equal to 0 and is, therefore, different from that of the parent function.
D
The range of the transformed function and the parent function are both all real numbers greater than or equal to 4 .

Explanation

The parent function f(x) = |x| is defined for every real number, so its domain is all real numbers. Multiplying its output by 0.3 and shifting it down 4 units do not restrict which x-values are allowed, so the transformed function also has domain all real numbers. Its range changes from y ≥ 0 to y ≥ −4, so the range statements in C and D are incorrect.

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