Answered

IDNLearn.com: Where your questions meet expert answers and community support. Our platform is designed to provide quick and accurate answers to any questions you may have.

Which statement is true about [tex][tex]\( f(x) = -\frac{2}{3} |x+4| - 6 \)[/tex][/tex]?

A. The graph of [tex][tex]\( f(x) \)[/tex][/tex] has a vertex of [tex][tex]\((-4, 6)\)[/tex][/tex].
B. The graph of [tex][tex]\( f(x) \)[/tex][/tex] is a horizontal stretch of the graph of the parent function.
C. The graph of [tex][tex]\( f(x) \)[/tex][/tex] opens upward.
D. The graph of [tex][tex]\( f(x) \)[/tex][/tex] has a domain of [tex][tex]\( x \leq -6 \)[/tex][/tex].

Which Statement Is True About Textex Fx Frac23 X4 6 TextexA The Graph Of Textex Fx Textex Has A Vertex Of Textex4 6textexB The Graph Of Textex Fx Textex Is A Ho class=

Sagot :

Answer: C

Step-by-step explanation:

Japtcidn

Answer:

The correct statement is B. The graph of [tex]f(x)=−

3

2

∣x+4∣−6 [/tex] is a horizontal stretch of the graph of the parent function.

Explanation:

[tex]f(x)=−

3

2

∣x+4∣−6 [/tex] is an absolute value function that has been horizontally stretched by a factor of 2/3 and vertically shifted down by 6 units.

The vertex of the graph is at (-4, -6), not (−4, 6) as stated in option A.

The graph opens downward, not upward as stated in option C.

The domain of the function is all real numbers, not [tex]x≤−6 [/tex] as stated in option D.

Therefore, the correct statement is that the graph is a horizontal stretch of the parent absolute value function.

We appreciate your contributions to this forum. Don't forget to check back for the latest answers. Keep asking, answering, and sharing useful information. Thanks for visiting IDNLearn.com. We’re dedicated to providing clear answers, so visit us again for more helpful information.