Graph y=5^(-x)

Problem

y=5(−x)

Solution

1. Identify the type of function. This is an exponential decay function because the base 5 is raised to a negative exponent, which can be rewritten as y=(1/5)x

2. Determine the horizontal asymptote. As x increases toward infinity, 5(−x) approaches 0 Therefore, the horizontal asymptote is the line y=0

3. Calculate the y-intercept by substituting x=0

y=5

y=1

The y-intercept is (0,1)

4. Find additional points to determine the shape.
   For x=1

y=5(−1)

y=1/5

For x=−1

y=5(−(−1))

y=5

5. Sketch the graph by plotting the points (−1,5) (0,1) and (1,0.2) then drawing a smooth curve that approaches the x-axis as x increases.

Final Answer

y=5(−x)

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