Question
Which function is a horizontal compression of its parent function of f(x)=x^7 by a factor of 4?
Answers
GPT-4o mini
To achieve a horizontal compression of a function by a factor of \( k \), you need to replace the variable \( x \) with \( \frac{x}{k} \).
For the parent function \( f(x) = x^7 \), to compress it horizontally by a factor of 4, you would replace \( x \) with \( \frac{x}{4} \):
\[
f\left(\frac{x}{4}\right) = \left(\frac{x}{4}\right)^7
\]
This simplifies to:
\[
f\left(\frac{x}{4}\right) = \frac{x^7}{4^7} = \frac{x^7}{16384}
\]
Thus, the function that represents a horizontal compression of the parent function \( f(x) = x^7 \) by a factor of 4 is:
\[
f(x) = \left(\frac{x}{4}\right)^7 = \frac{x^7}{16384}
\]
For the parent function \( f(x) = x^7 \), to compress it horizontally by a factor of 4, you would replace \( x \) with \( \frac{x}{4} \):
\[
f\left(\frac{x}{4}\right) = \left(\frac{x}{4}\right)^7
\]
This simplifies to:
\[
f\left(\frac{x}{4}\right) = \frac{x^7}{4^7} = \frac{x^7}{16384}
\]
Thus, the function that represents a horizontal compression of the parent function \( f(x) = x^7 \) by a factor of 4 is:
\[
f(x) = \left(\frac{x}{4}\right)^7 = \frac{x^7}{16384}
\]