Analyze the effect on the graph when $$ f(x)=x^{3} $$ is replaced with $$ f(x)=(b x)^{3} $$ where $$ b1 $$. Which option correctly describes the effect? (1 point) the graph is shifted to the left the graph is horizontally compressed the graph is horizontally stretched the graph is shifted to the right

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Analyze the effect on the graph when $$ f(x)=x^{3} $$ is replaced with $$ f(x)=(b x)^{3} $$ where $$ b>1 $$. Which option correctly describes the effect? (1 point) the graph is shifted to the left the graph is horizontally compressed the graph is horizontally stretched the graph is shifted to the right

UpStudy AI · Accepted Answer

When $$ f(x) = x^3 $$ is replaced with $$ f(x) = (b x)^3 $$ where $$ b > 1 $$, the transformation can be analyzed as follows:

$$
f(x) = (b x)^3 = b^3 x^3
$$

Here, the coefficient $$ b^3 $$ affects the vertical scaling of the graph, making it steeper. However, focusing on the horizontal aspect:

- Replacing $$ x $$ with $$ b x $$ results in a horizontal compression by a factor of $$ \frac{1}{b} $$.

Since $$ b > 1 $$, the graph becomes horizontally compressed.

**Correct Option:**  
the graph is horizontally compressed
The graph is horizontally compressed.

Analyze the effect on the graph when is replaced with
where . Which option correctly describes the effect? (1 point)
the graph is shifted to the left
the graph is horizontally compressed
the graph is horizontally stretched
the graph is shifted to the right

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Analyze the effect on the graph when is replaced with where . Which option correctly describes the effect? (1 point) the graph is shifted to the left the graph is horizontally compressed the graph is horizontally stretched the graph is shifted to the right