Question

Which statement is true about f(x)=-2/3 |x+4|-8?

a) The graph is a horizontal stretch by a factor of 2/3.
b) The graph is a vertical compression by a factor of 2/3.
c) The graph is a vertical stretch by a factor of 2/3.
d) The graph is a horizontal compression by a factor of 2/3.

Answer 1

The graph of the function f(x)=-2/3 |x+4|-8 is a vertical stretch by a factor of 2/3.

Step-by-step explanation:

The statement that is true about the function f(x)=-2/3 |x+4|-8 is option (c) The graph is a vertical stretch by a factor of 2/3.

To understand why, let's break down the function:

• The absolute value function, |x+4|, represents the distance between x and -4 on the number line, always resulting in a positive value.
• Multiplying this absolute value by -2/3 reflects the function about the x-axis and scales it vertically by a factor of 2/3.
• Finally, subtracting 8 shifts the graph downward by 8 units.

Combining these transformations, we can conclude that the graph of f(x)=-2/3 |x+4|-8 is a vertical stretch by a factor of 2/3.