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The function [tex]f(x) = 2^x - 1[/tex] is transformed to function [tex]g[/tex] through a horizontal shift of 7 units left. What is the equation of function [tex]g[/tex]?

Replace the values of [tex]h[/tex] and [tex]k[/tex] in the equation:

[tex]g(x) = 2^{x+h} + k[/tex]

Sagot :

GinnyAnswer
To find the new function \( g(x) \) when the original function \( f(x) = 2^x - 1 \) undergoes a horizontal shift of 7 units to the left, we need to follow these steps:

1. Understand the transformation:
- A horizontal shift of 7 units to the left means we replace \( x \) with \( x + 7 \) in the original function.

2. Apply the transformation to the original function:
- The original function is \( f(x) = 2^x - 1 \).
- Replacing \( x \) with \( x + 7 \), the function becomes \( 2^{(x + 7)} - 1 \).

3. Form the new function \( g(x) \):
- With the applied shift, the new function \( g(x) \) can be written as \( g(x) = 2^{(x + 7)} - 1 \).

Thus, the transformed function \( g(x) \) is:

[tex]\[ g(x) = 2^{(x + 7)} - 1 \][/tex]
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