Graph y=5^x

Problem

y=5

Solution

1. Identify the type of function. This is an exponential function of the form y=bx where the base b=5 Since b>1 the graph represents exponential growth.

2. Determine the y-intercept. To find the y-intercept, substitute x=0 into the equation.

y=5

y=1

The graph passes through the point (0,1)

3. Calculate additional points to define the shape. Choose small integer values for x
   For x=1

y=5=5

For x=−1

y=5(−1)=1/5=0.2

The points are (1,5) and (−1,0.2)

4. Identify the horizontal asymptote. As x becomes more negative, 5 approaches 0 but never reaches it.

Horizontal Asymptote: *y=0

5. Sketch the curve. Start near the x-axis on the left side, pass through (0,1) and (1,5) and rise steeply to the right.

Final Answer

y=5

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