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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=


Answer :

Answer: C

Step-by-step explanation:

japtc

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.

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