The graph of f, of, x, equals, minus, 2, to the power xf(x)=−2 
x
  is given below. Write the equation of a function g, of, xg(x) which would shift the graph of f, of, xf(x) left 1 unit.

To shift the graph of \( f(x) = -2^x \) left by 1 unit, we modify the input variable \( x \) by adding 1 inside the function. A leftward shift of the graph is achieved by replacing \( x \) with \( x+1 \) in the function's equation.

Thus, the equation of the function \( g(x) \) that represents the graph of \( f(x) \) shifted left by 1 unit is:

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

This transformation shifts the graph of \( f(x) = -2^x \) left by 1 unit.

Do you have any questions or want more details on this? Here are some related questions for further understanding:

1. How would shifting the graph right by 2 units affect the equation of \( f(x) \)?
2. What happens to the graph if we shift it up or down?
3. How can we reflect the graph of \( f(x) \) across the x-axis?
4. What is the effect of changing the base from 2 to another number?
5. How does the graph of \( g(x) = -2^{x+1} \) differ visually from \( f(x) = -2^x \)?

**Tip**: Shifting a graph left or right always involves changing the variable inside the function's input, while up/down shifts modify the output directly.

The graph of f(x) = -2^x is given below. Write the equation of a function g(x) which would shift the graph of f(x) left 1 unit.

Discover how to shift the graph of the exponential function f(x) = -2^x left by 1 unit. This guide explains the concept of graph shifting and provides a step-by-step solution using the transformation g(x) = -2^{x+1}. Suitable for students in Grades 9-11.

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