Graph y=0.45^x

Problem

y=0.45

Solution

1. Identify the type of function. This is an exponential function of the form y=bx where the base b=0.45 Since 0<0.45<1 the graph represents exponential decay.

2. Determine the y-intercept. When x=0 y=0.45=1 The graph passes through the point (0,1)

3. Calculate additional points to define the shape. For x=1 y=0.45=0.45 For x=−1 y=0.45(−1)=1/0.45≈2.22

4. Identify the horizontal asymptote. As x increases toward infinity, 0.45 approaches 0 The horizontal asymptote is the x-axis, y=0

5. Sketch the curve. Draw a smooth curve that decreases from left to right, passing through (−1,2.22) (0,1) and (1,0.45) while flattening out along the positive x-axis.

Final Answer

y=0.45

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