Question

1. given the equation $y = 2|x + 4| - 5$, describe the transformations on the parent function $y = |x|$. stretch 2, left 4, down 5 3pts

Explanation:

Step1: Analyze vertical stretch/compression

For a function \( y = a|x - h| + k \), the coefficient \( a \) affects vertical stretch. Here \( a = 2 \), so the parent function \( y = |x| \) is vertically stretched by a factor of 2 (since \( |a|>1 \)).

Step2: Analyze horizontal shift

The term \( x + 4 \) can be written as \( x - (- 4) \). For horizontal shifts, \( h \) in \( y = |x - h| \) determines the shift. Here \( h=-4 \), so the graph shifts 4 units to the left (since shifting left is when \( h \) is negative in \( x - h \) form).

Step3: Analyze vertical shift

The constant term \( - 5 \) (from \( y = 2|x + 4|-5 \)) means the graph shifts 5 units down (because subtracting 5 from the function value moves it down vertically).

Answer:

The transformations on the parent function \( y = |x| \) to get \( y = 2|x + 4|-5 \) are: a vertical stretch by a factor of 2, a horizontal shift 4 units to the left, and a vertical shift 5 units down.