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(5pts) Describe how the graph of
g(x)=-(8x^(-7))+3 is related to the graph of
f(x)=8^(x).

( $5$ pts) Describe how the graph of $g(x)=-\left(8 x^{-7}\right)+3$ is related to the graph of $f(x)=8^{x}$ .

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Find the vertex of the transformed function

Full solution

Q. (

5

pts) Describe how the graph of

g(x)=-\left(8 x^{-7}\right)+3

is related to the graph of

f(x)=8^{x}

.

Identify Function Types: $g(x)$ is given as $-8x^{-7} + 3$ , and $f(x)$ is given as $8^{x}$ . First, notice that $g(x)$ is not an exponential function like $f(x)$ , it's a rational function because of the negative exponent.
Analyze Graph of $g(x)$ : The graph of $g(x)$ will look different from $f(x)$ because $g(x)$ involves $x$ to the power of $-7$ , which means it will have a horizontal asymptote at $y = 3$ and will approach zero as $x$ increases or decreases.
Analyze Graph of $f(x)$ : The graph of $f(x)$ is an exponential growth function since the base, $8$ , is greater than $1$ . It will increase rapidly as $x$ increases.
Consider Sign Differences: The negative sign in front of $g(x)$ indicates a reflection over the $x$ -axis compared to if it were positive. So, $g(x)$ will be decreasing as $x$ moves away from $0$ , unlike $f(x)$ which is increasing as $x$ increases.
Summary of Functions: To summarize, $g(x)$ is a rational function with a horizontal asymptote and reflection over the $x$ -axis, while $f(x)$ is an exponential growth function without these features.

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