Graph y=-4^x

Problem

y=−4

Solution

1. Identify the parent function as y=4 which is an exponential growth function that passes through (0,1) and (1,4) with a horizontal asymptote at y=0

2. Apply the transformation, which is a reflection across the xaxis due to the negative sign in front of the base. Note that the negative is not part of the base, so −4 means −(4)

3. Determine the horizontal asymptote, which remains at y=0 because there is no vertical shift.

4. Calculate key points for the graph by substituting values for x
   If x=−1 y=−4(−1)=−0.25
   If x=0 y=−4=−1
   If x=1 y=−4=−4

5. Plot the points (−1,−0.25) (0,−1) and (1,−4) and draw a smooth curve that approaches y=0 as x goes to negative infinity and decreases rapidly as x increases.

Final Answer

y=−4

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