Ask a New Question
Menu

Given the function f(x)=x3

, analyze the changes in the graph to determine which statement best describes the graph of g(x)=−12f(x)
.(1 point)
Responses

The graph will undergo a reflection due to the negative sign, and a vertical compression because 0<|a|<1
.
The graph will undergo a reflection due to the negative sign, and a vertical compression because 0 is less than absolute value of A comma absolute value of A is less than 1 .

The graph will undergo a vertical stretch because 0<|a|<1
.
The graph will undergo a vertical stretch because 0 is less than absolute value of A comma absolute value of A is less than 1 .

The graph will only undergo a reflection due to the negative sign.
The graph will only undergo a reflection due to the negative sign.

The graph will undergo a reflection due to the negative sign, and a vertical stretch because |a|>1
.

1 answer

To analyze the transformation of the function \( f(x) = x^3 \) to \( g(x) = -12f(x) \), let's break it down step by step.

  1. Reflection: The negative sign in front of \( f(x) \) indicates that the graph will be reflected across the x-axis. This means that all y-values will be negated.

  2. Vertical Stretch/Compression: The factor of \(-12\) means that we also multiply the output of \( f(x) \) by 12 (and then reflect it). Since \( |a| = 12 > 1 \), this transformation involves a vertical stretch.

In summary:

  • The graph of \( g(x) = -12f(x) \) will indeed undergo a reflection across the x-axis due to the negative sign.
  • Additionally, it will undergo a vertical stretch because the absolute value of the constant (12) is greater than 1.

Thus, the best description of the transformation from \( f(x) = x^3 \) to \( g(x) = -12f(x) \) is:

The graph will undergo a reflection due to the negative sign, and a vertical stretch because |a| > 1.