Graph y=4^(x-1)

Problem

y=4(x−1)

Solution

1. Identify the parent function as y=4 which is an exponential growth function because the base 4 is greater than 1

2. Determine the horizontal shift by looking at the exponent x−1 Setting x−1=0 gives x=1 indicating the graph is shifted 1 unit to the right.

3. Find the horizontal asymptote. Since there is no vertical shift added to the exponential term, the horizontal asymptote remains at y=0

4. Calculate the y-intercept by substituting x=0 into the equation: y=4(0−1)=4(−1)=1/4

5. Plot key points to define the shape:

• When x=1 y=4(1−1)=4=1

• When x=2 y=4(2−1)=4=4

6. Sketch the curve passing through (0,0.25) (1,1) and (2,4) approaching the x-axis (y=0 as x moves toward negative infinity.

Final Answer

y=4(x−1)

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