Graph 4^x

Problem

y=4

Solution

1. Identify the type of function, which is an exponential growth function because the base 4 is greater than 1

2. Determine the y-intercept by substituting x=0 into the equation, giving y=4=1

3. Calculate additional points to define the shape of the curve, such as x=1⇒y=4=4 and x=−1⇒y=4(−1)=0.25

4. Identify the horizontal asymptote, which is the line y=0 (the x-axis), as 4 approaches 0 when x becomes a large negative number.

5. Sketch the curve passing through the points (−1,0.25) (0,1) and (1,4) ensuring it rises steeply to the right and flattens toward the x-axis to the left.

Final Answer

y=4

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