Question

if the graph of $f(x) = |x|$ is stretched vertically by a factor of 5 and shifted 2 units to the left, which function represents the new graph? select the correct answer. $\bigcirc\\ g(x) = |5x| + 2$ $\bigcirc\\ g(x) = |5x - 2|$ $\bigcirc\\ g(x) = 5|x| - 2$ $\bigcirc\\ g(x) = 5|x + 2|$

Explanation:

Step1: Vertical stretch by factor 5

Multiply the function by 5: $5|x|$

Step2: Shift left by 2 units

Replace $x$ with $x+2$: $5|x+2|$

Answer:

D. $g(x) = 5|x + 2|$