Question
of 5 The graph of \( f(x)=x^{3} \) is transformed by multiplying the function by a factor of \( a=\frac{1}{4} \). Identify the new coordinate for \( x=4 \) after \( f(x) \) is vertically compressed. (1 point) The new coordinates are ( \( \square, \square) \).
Ask by French Lang. in the United States
Jan 23,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The new coordinates are (4, 16).
Solution
After vertically compressing the function \( f(x) = x^3 \) by a factor of \( \frac{1}{4} \), the new function becomes:
\[
f_{\text{new}}(x) = \frac{1}{4}x^3
\]
To find the new coordinate for \( x = 4 \):
\[
f_{\text{new}}(4) = \frac{1}{4} \times 4^3 = \frac{1}{4} \times 64 = 16
\]
**The new coordinates are (4, 16).**
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Simplify this solution Bonus Knowledge
When the function \( f(x) = x^{3} \) is vertically compressed by a factor of \( a = \frac{1}{4} \), the new function becomes \( g(x) = \frac{1}{4} f(x) = \frac{1}{4} x^{3} \). To find the new coordinate for \( x = 4 \), we substitute \( 4 \) into the transformed function: \( g(4) = \frac{1}{4} (4^{3}) = \frac{1}{4} (64) = 16 \). So, the new coordinates are \( (4, 16) \).
