Question

What statement is true about

f(x)=−6∣x+5∣−2?

a) The graph of f(x) is a horizontal compression of the graph of the parent function.
b) The graph of f(x) is a horizontal stretch of the graph of the parent function.
c) The graph of f(x) opens upward.
d) The graph of f(x) opens to the right.

Answer 1

The graph of f(x) = -6|x+5| - 2 is a horizontal compression of the graph of the parent function.

Step-by-step explanation:

The statement that is true about f(x) = -6|x+5| - 2 is a) The graph of f(x) is a horizontal compression of the graph of the parent function.

To understand this, let's break it down. The parent function of f(x) is |x| (the absolute value function). When we have a negative sign in front of the absolute value function, it reflects the graph over the x-axis, making it open downwards. The value of 6 in front of the absolute value function is the compression factor, which means the graph of f(x) is compressed horizontally by a factor of 6.

So, the graph of f(x) is a horizontally compressed, reflected, and downward-opening graph compared to the parent function.