Asked by Mackenzie Kiser on Mar 10, 2024
Verified
Identify the transformation of f′(x) =2xf ^ { \prime } ( x ) = 2 ^ { x }f′(x) =2x . h(x) =2x−6h ( x ) = 2 ^ { x - 6 }h(x) =2x−6
A) a shift of 6 units downward
B) a shift of 6 units to the left
C) a reflection about the line x=6
D) a shift of 6 units to the right
E) a shift of 6 units upward
Transformation
A process by which a shape is changed through operations such as rotation, reflection, translation, or resizing, altering its position or size but not its fundamental characteristics.
- Understand the concept of transformations applied to exponential functions.
Verified Answer
AR
Allison RominMar 10, 2024
Final Answer :
D
Explanation :
The original function is a basic exponential function where the base is 2 and the exponent is x. The transformed function is also an exponential function with the same base, but the exponent is now (x-6). This means that the graph of h(x) is the same as the graph of f(x) shifted 6 units to the right. Therefore, the correct answer is D, a shift of 6 units to the right.
Learning Objectives
- Understand the concept of transformations applied to exponential functions.
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