Graph y=4*2^x

Problem

y=4⋅2

Solution

1. Identify the type of function. This is an exponential function of the form y=a⋅bx where a=4 and b=2 Since b>1 the graph represents exponential growth.

2. Determine the y-intercept by setting x=0

y=4⋅2

y=4⋅1

y=4

The y-intercept is at the point (0,4)

3. Calculate additional points to define the shape of the curve.
   For x=1

y=4⋅2=8

For x=2

y=4⋅2=16

For x=−1

y=4⋅2(−1)=2

For x=−2

y=4⋅2(−2)=1

4. Identify the horizontal asymptote. As x approaches negative infinity, 2 approaches 0 so y approaches 0 The horizontal asymptote is the line y=0 (the x-axis).

5. Sketch the graph by plotting the points (−2,1) (−1,2) (0,4) (1,8) and (2,16) then drawing a smooth curve that rises from left to right and approaches the x-axis on the left.

Final Answer

y=4⋅2

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