Answer :
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]
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]
