The function is a dilation of the original function y=2x . Which of the following correctly explains the transformation?

Question

(1 point)
Responses

Use the coordinates to show that each point has been dilated using the rule y=2x+k, where k=4.
Use the coordinates to show that each point has been dilated using the rule y equals 2 superscript x baseline plus k , where k equals 4 .

Use the coordinates to show that each point has been dilated using the rule y=k⋅2x, where k=4.
Use the coordinates to show that each point has been dilated using the rule y equals k times 2 superscript x baseline , where k equals 4 .

Use the coordinates to show that each point has been dilated using the rule y=k⋅2x, where k=14.
Use the coordinates to show that each point has been dilated using the rule y equals k times 2 superscript x baseline , where k equals Start Fraction 1 over 4 End Fraction .

Use the coordinates to show that each point has been dilated using the rule y=2x−k, where k=4.

Answer 1

To explain the transformation involved in dilating the function \( y = 2x \), we need to understand the different types of transformations that can be applied to a function. A dilation, in general, involves multiplying the function's output (the y-value) by a constant \( k \).

The correct explanation for a dilation of the original function \( y = 2x \) using a constant \( k \) would be:

Use the coordinates to show that each point has been dilated using the rule \( y = k \cdot 2^x \), where \( k = 4 \).

This means that every output value of the original function \( y = 2x \) is being multiplied by 4, leading to the transformed function \( y = 4 \cdot 2^x \).