Answer:
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."
Step-by-step 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.
Answer:
The domain of the transformed function and the parent function are both all real numbers.
Step-by-step 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)
