Question

Which statement is true about "f(x)"

Answer 1

ANSWER

The graph of f(x) is horizontally stretched.

EXPLANATION

The given function is

$f(x) = - \frac{2}{3} |x + 4| - 6$

The vertex of this function is (-4,-6)

The factor ⅔ strectches the graph horizontally in the graph of f(x) opens wider than the parent function

y=|x|

The negative factor will make the graph open downwards. It is a reflection in the x-axis.

The domain of the graph is all real numbers.

Answer 2

Answer: Second Option

The graph of f(x) is horizontally stretched.

Step-by-step explanation:

We have the function:

$f(x) = -\frac{2}{3}|x+4| - 6$

The main function $y=|x|$ has its vertex in the point (0,0) opens upwards and its domain is all real numbers.

Notice that $f(x) = -\frac{2}{3}|x+4| - 6$ is a transformation of the function $y=|x|$.

Observe the attached image. Where the red line represents the transformed function. Notice that it opens down and is stretched horizontally. Its vertex is at point (4, -6) and the domain is all real numbers

Therefore the statement that is true is the second

The graph of f(x) is horizontally stretched.