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B.) Let
g be a reflection in the
y-axis followed by a translation 4 units left, followed by a horizontal stretch by a factor of 3 and a vertical compression by a factor of
1//2 of the graph of
f(x)=log ((1)/(2)x)+8

B.) Let $g$ be a reflection in the $y$ -axis followed by a translation $4$ units left, followed by a horizontal stretch by a factor of $3$ and a vertical compression by a factor of $1 / 2$ of the graph of $f(x)=\log \frac{1}{2} x+8$

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Function transformation rules

Full solution

Q. B.) Let

g

be a reflection in the

y

-axis followed by a translation

4

units left, followed by a horizontal stretch by a factor of

3

and a vertical compression by a factor of

1 / 2

of the graph of

f(x)=\log \frac{1}{2} x+8

Reflect in y-axis: Reflect $f(x)$ in the y-axis. $f(x) = \log(\frac{1}{2}x) + 8$ becomes $f(-x) = \log(\frac{1}{2}(-x)) + 8$ .
Translate $4$ units left: Translate $f(x)$ $4$ units left. $\newline$ $f(-x) = \log((\frac{1}{2})(-x)) + 8$ becomes $f(-x - 4) = \log((\frac{1}{2})(-x - 4)) + 8$ .
Horizontal stretch by $3$ : Apply a horizontal stretch by a factor of $3$ . $f(-x - 4) = \log((\frac{1}{2})(-x - 4)) + 8$ becomes $f(-3x - 4) = \log((\frac{1}{2})(-3x - 4)) + 8$ .
Vertical compression by $\frac{1}{2}$ : Apply a vertical compression by a factor of $\frac{1}{2}$ . $f(-3x - 4) = \log(\left(\frac{1}{2}\right)(-3x - 4)) + 8$ becomes $\frac{1}{2}f(-3x - 4) = \frac{1}{2}\log(\left(\frac{1}{2}\right)(-3x - 4)) + 4$ .

More problems from Function transformation rules

Question

g(x)

g(x)

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f(x)=9|x+2|-4

\newline

\newline

\text{}(A)g(x) = 9|x+2| - 4\text{]}

\newline

\text{}(B)g(x) = 9|x-2| - 4\text{]}

\newline

\text{}(C)g(x)=-9|x-2| +4\text{]}

\newline

\text{(D)}g(x) = -9|x + 2| + 4\text{]}

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\text{translates it } 4 \text{ units right}

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\text{translates it } 4 \text{ units down}

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Question

What kind of transformation converts the graph of

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Question

y=x^{2}

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What is the equation of the new parabola?

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Question

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