Question

identify if the graph of the logarithmic function flips or stays the same.
$f(x)=-\frac{2}{3}log(x + 3)-8$

a. the graph will stay the same.

b. the graph will stay the same because a = -2/3 and -2/3 is positive.

c. the graph will flip because a = -2/3 and -2/3 is between 0 and 1.

d. the graph will flip because a = -2/3 and -2/3 is negative.

3/8

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Explanation:

Step1: Recall graph - transformation rule

For a logarithmic function of the form $y = a\log(x - h)+k$, if $a>0$, the graph has the same general shape as the parent - function $y=\log(x)$, and if $a < 0$, the graph is reflected (flips) over the $x$ - axis.

Step2: Analyze the value of $a$ in the given function

In the function $f(x)=-\frac{2}{3}\log(x + 3)-8$, the value of $a=-\frac{2}{3}$. Since $a =-\frac{2}{3}<0$, the graph of the function will flip over the $x$ - axis.

Answer:

D. The graph will flip because a = -2/3 and -2/3 is negative.