Question

4. Given the parent function as h(x)= 1x6^x, state the transformations given the new function listed below. You can list each transformation in the provided bullet point.

h'(x) = 2x6^x-3 + 4

Answer 1

The new function h'(x) = 2x6^x-3 + 4 has undergone a vertical stretch by a factor of 2, a horizontal shift 3 units to the right, and a vertical shift 4 units upwards compared to the parent function h(x) = x6^x.

Step-by-step explanation:

The transformations of the function h'(x) = 2x6^x-3 + 4 relative to the parent function h(x) = x6^x can be identified step by step:

• The coefficient 2 in front of x indicates a vertical stretch by a factor of 2.
• The -3 added to x in the exponent of 6 signals a horizontal shift 3 units to the right.
• The constant +4 outside the function represents a vertical shift 4 units upwards.