Graph y=2^x-1

Problem

y=2−1

Solution

1. Identify the parent function as y=2 which is a basic exponential growth function with a horizontal asymptote at y=0

2. Determine the vertical shift by looking at the constant term −1 which moves the entire graph and the horizontal asymptote down by 1 unit.

3. Find the new horizontal asymptote, which is now the line y=−1

4. Calculate the y-intercept by substituting x=0 into the equation.

y=2−1

y=1−1

y=0

5. Calculate additional points to determine the shape of the curve, such as when x=1 and x=2

y=2−1=1

y=2−1=3

6. Sketch the curve passing through (0,0) (1,1) and (2,3) approaching the line y=−1 as x decreases toward negative infinity.

Final Answer

y=2−1

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