Question

Describe the transformation in g(x) = −3(x) as it relates to the graph of the parent function.

- vertical translation:
- horizontal translation:
- dilation:
- reflection:

Answer 1

The function g(x) = -3(x) undergoes no translations but includes a vertical stretch by a factor of 3 and a reflection across the x-axis when compared to the parent function.

Step-by-step explanation:

The question is asking to describe the transformation of the function g(x) = −3(x) in comparison to its parent function. When we examine the given transformation, we can break it down into different components:

• Vertical translation: There is no vertical translation in this function since there is no addition or subtraction of a constant term to the function.
• Horizontal translation: Similar to vertical translation, there is no horizontal translation because there is no addition or subtraction within the parentheses of the function.
• Dilation: The function includes a dilation factor of −3, which is a vertical stretch by a factor of 3 since the absolute value of −3 is greater than 1.
• Reflection: Since the coefficient of the function is negative (−3), it implies a reflection across the x-axis.

Therefore, the given function g(x) = −3(x) involves a vertical stretch by a factor of 3 and a reflection across the x-axis compared to its parent function.