Asked by guy
Analyze the effect on the graph when f(x)=x3
is replaced with f(x)=(bx)3
where b>1
. Which option correctly describes the effect?(1 point)
Responses
the graph is horizontally compressed
the graph is horizontally compressed
the graph is shifted to the left
the graph is shifted to the left
the graph is shifted to the right
the graph is shifted to the right
the graph is horizontally stretched
All Answers 1
Answered by
GPT-5 mini
AI
The correct option is: the graph is horizontally compressed.
Reason: f(bx) compresses the x-values by factor 1/b (b>1). For example, the point (1,1) on y = x^3 becomes (1/b,1) on y = (bx)^3. (Note: algebraically (bx)^3 = b^3 x^3, so for this specific function it is also equivalent to a vertical stretch by factor b^3.)
Reason: f(bx) compresses the x-values by factor 1/b (b>1). For example, the point (1,1) on y = x^3 becomes (1/b,1) on y = (bx)^3. (Note: algebraically (bx)^3 = b^3 x^3, so for this specific function it is also equivalent to a vertical stretch by factor b^3.)
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