Question

The parent function f(x) = IxI is reflected across the x-axis, translated five units right, four units up and is vertically stretched. Which is the transformed function?

a) f(x)=-|x+4|-5
b) f(x) = - 1/3 |x-5|+4
c) f(x) = -|x +5|-4
d) f(x) = - 5/3 | x-5 | +4

Answer 1

The transformed function after reflecting the parent function f(x)=|x| across the x-axis, translating it five units right and four units up, and applying a vertical stretch is d) f(x) = -\(\frac{5}{3}\)|x - 5| + 4.

Step-by-step explanation:

To determine which of the given functions represents the transformed function, we need to apply the transformations one by one to the parent function f(x) = |x|. The parent function is a reflection across the x-axis, which changes the function to f(x) = -|x|. Then, the function is translated five units to the right, which is represented by changing the argument from x to (x - 5), resulting in f(x) = -|x - 5|. A translation of four units up adds 4 to the function: f(x) = -|x - 5| + 4. Finally, a vertical stretch means the absolute value portion of the function is multiplied by a factor greater than one, but since the problem doesn't provide us with the specific factor, let's denote it as 'a'; thus, f(x) = -a|x - 5| + 4. Option d) f(x) = -\(\frac{5}{3}\)|x - 5| + 4 matches our transformed function with a vertical stretch factor of \(\frac{5}{3}\).