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Chapter 5: Q. 90 (page 285)

Find an exponential function with horizontal asymptote y=-3whose graph contains the points (0,-2)and (-2,1).

Short Answer

Expert verified

The exponential functions are(12)x-3and(-12)x-3.

Step by step solution

01

Step 1. Using given information.

Consider the given horizontal asymptote y=-3.

And given the two points on the exponential function are role="math" localid="1646284018344" (0,-2)and (-2,1).

If the horizontal asymptote is y=0, then the exponential function is y=ax.

If the horizontal asymptote is y=-3, then the exponential function is y=ax-3.

02

Step 2. Finding exponential function.

At (-2,1), the exponential function is

1=a-2-31+3=a-2a-2=41a2=4a2=14a=卤12

So the exponential functions arey=(12)x-3andy=(-12)x-3.

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Most popular questions from this chapter

Vehicle Stopping Distance Taking into account reaction time, the distance d(in feet) that a car requires to come to a complete stop while traveling rmiles per hour is given by the function

localid="1646198784356" d(r)=6.97r-90.39

a. Express the speed rat which the car is traveling as a function of the distance localid="1646198792401" drequired to come to a complete stop

b. Verify that localid="1646198797631" r=r(d)is the inverse of localid="1646198802104" d=d(r)by showing that localid="1646198806352" r(d(r))=rand localid="1646198811055" d(r(d))=d

c. Predict the speed that a car was traveling if the distance required to stop was localid="1646198818232" 300feet.

d(r(d))=d

The graph of an exponential function is given. Match each graph to one of the following functions.

Begin with the graph of y=exand use transformation to graph the function. Determine the domain, range and horizontal asymptote of the function.

fx=7-3e2x

If fx=ax, show that fA+B=fA.fB.

solve each equation. Verify your results using a graphing utility.

4x2=2x
See all solutions

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