Identify the transformation of f ′ ( x ) = 2 x f ^ { \prime } ( x ) = 2 ^ { x } f ′ ( x ) = 2 x . h ( x ) = 2 x − 6 h ( x ) = 2 ^ { x - 6 } h ( x ) = 2 x − 6 A) a shift of 6 units downwardB) a shift of 6 units to the leftC) a reflection about the line x=6D) a shift of 6 units to the rightE) a shift of 6 units upward

Question

Identify the transformation of   f ′ ( x )  = 2 x f ^ { \prime } ( x )  = 2 ^ { x } f ′ ( x )  = 2 x   .   h ( x )  = 2 x − 6 h ( x )  = 2 ^ { x - 6 } h ( x )  = 2 x − 6 A) a shift of 6 units downwardB) a shift of 6 units to the leftC) a reflection about the line x=6D) a shift of 6 units to the rightE) a shift of 6 units upward

Allison Romin · Accepted Answer

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.

Identify the transformation of $\prime } ( x ) = 2 ^ { x }$ . $h ( x ) = 2 ^ { x - 6 }$

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

Definitions

Learning Objectives

Learning Objectives

Related questions

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 downwardB) a shift of 6 units to the leftC) a reflection about the line x=6D) a shift of 6 units to the rightE) a shift of 6 units upward

Definitions

Learning Objectives

Learning Objectives

Related questions

Identify the transformation of $\prime } ( x ) = 2 ^ { x }$ . $h ( x ) = 2 ^ { x - 6 }$

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