Question

he graph of f(x) = |x| is stretched by a factor of 0.3 and translated down 4 units. Which statement about the domain and range of each function is correct? The range of the transformed function and the parent function are both all real numbers greater than or equal to 4. The domain of the transformed function is all real numbers and is, therefore, different from that of the parent function. 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. The domain of the transformed function and the parent function are both all real numbers.

Answer 1

The domain of the transformed function and the parent function are both all real numbers.

Explanation:

Stretching a function by any factor doesn't change either its domain nor its range.

Translating up or down a function changes its range. In this case, the lowest value the parent function can take is 0 when x=0; after translation, for x = 0 then f(x) = -4. Therefore,

f(x) = |x|

domain = all real numbers

range = [0, infinity)

f(x) = 0.3*|x| - 4

domain = all real numbers

range = [-4, infinity)

Answer 2

Out of the four, the only statement true about the parent and the transformed function is:

"The domain of the transformed function and the parent function are all real numbers."

Explanation:

Parent function:

f(x) = |x|

Applying transformations:

1. Stretched by a factor of 0.3:

f(x) = 3|x|

2. Translated down 4 units:

f(x) = 3|x| - 4

Transformed function:

f(x) = 3|x| - 4

We can see that:

Range of the parent function = All real numbers greater than or equal to 0.

Range of the transformed function = All real numbers greater than or equal to -4.

Domain of the parent and the transformed function is same and equal to all real numbers.

Hence, the first three statements are wrong and the fourth one is true.