Answered

Let f (x) = 8x. The graph of f(x) is transformed into the graph of g(x) by a vertical stretch of 4 and a translation of 7 units down. What is the equation for g(x)? Enter your answer in the box.

Answer :

ANSWER

[tex]g(x)=32x-7[/tex]

EXPLANATION

We want to find the equation for g(x).

First, the function is stretched vertically by a factor of 4. This means that the function changes as follows:

[tex]f(x)\to4f(x)[/tex]

Therefore, the function becomes:

[tex]\begin{gathered} 4(8x) \\ \Rightarrow32x \end{gathered}[/tex]

Then, it is translated 7 units down. This means that the function changes as follows:

[tex]f(x)\to f(x)-7[/tex]

Therefore, the equation for g(x) is:

[tex]g(x)=32x-7[/tex]

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