Graph y=(1/2)^x+6

Problem

y=(1/2)^x+6

Solution

1. Identify the parent function and its transformations. The base function is y=(1/2)^x which represents exponential decay because the base is between 0 and 1

2. Determine the horizontal asymptote by looking at the vertical shift. The +6 shifts the entire graph up by 6 units, moving the horizontal asymptote from y=0 to y=6

3. Find the y-intercept by substituting x=0 into the equation.

y=(1/2)^0+6

y=1+6=7

4. Calculate additional points to determine the shape of the curve. For x=−1

y=(1/2)^(−1)+6=2+6=8

For x=1

y=(1/2)^1+6=0.5+6=6.5

5. Sketch the graph by plotting the points (−1,8) (0,7) and (1,6.5) then drawing a smooth curve that approaches the line y=6 as x increases toward infinity.

Final Answer

y=(1/2)^x+6

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