Question

Which function represents a horizontal compression by a factor of 17
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7
of the function g(x)=−(x−1)3+2
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?(1 point)
Responses

j(x)=−(17(x−1))3+2
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j left parenthesis x right parenthesis equals negative left parenthesis start fraction 1 over 7 end fraction left parenthesis x minus 1 right parenthesis right parenthesis superscript 3 baseline plus 2

h(x)=−(7(x−1))3+2
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h left parenthesis x right parenthesis equals negative left parenthesis 7 left parenthesis x minus 1 right parenthesis right parenthesis superscript 3 baseline plus 2

k(x)=−(17x−1)3+2
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k left parenthesis x right parenthesis equals negative left parenthesis start fraction 1 over 7 end fraction x minus 1 right parenthesis superscript 3 baseline plus 2

m(x)=−(7x−1)3+2

Answer 1

To find the function that represents a horizontal compression by a factor of \( \frac{1}{17} \) of the function \( g(x) = - (x - 1)^3 + 2 \), we need to understand how horizontal transformations affect the function.

A horizontal compression by a factor \( c \) transforms the function \( g(x) \) into \( g(kx) \), where \( k = \frac{1}{c} \). In this case, since the compression factor is \( \frac{1}{17} \), we set \( c = 17 \) and substitute into the function:

1. Identify the transformation: \( g(kx) = -((kx) - 1)^3 + 2 \).
2. Substitute \( k = 17 \): \( g(17x) = -((17x) - 1)^3 + 2 \).

So, the function that represents a horizontal compression by a factor of \( 17 \) of \( g(x) \) is:

\[
j(x) = - (17(x - 1))^3 + 2
\]

Among the options provided, the correct choice is:

**j(x) = - (17(x - 1))^3 + 2**