Chapter 5: Q. 90 (page 285)

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

Short Answer

Expert verified

The exponential functions are ${(\frac{1}{2})}^{x} - 3$ and ${(- \frac{1}{2})}^{x} - 3$ .

Step by step solution

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 $y = a^{x}$ .

If the horizontal asymptote is $y = - 3$ , then the exponential function is $y = a^{x} - 3$ .

Step 2. Finding exponential function.

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

$1 = a^{- 2} - 3 1 + 3 = a^{- 2} a^{- 2} = 4 \frac{1}{a^{2}} = 4 a^{2} = \frac{1}{4} a = \pm \frac{1}{2}$

So the exponential functions are $y = {(\frac{1}{2})}^{x} - 3$ and $y = {(- \frac{1}{2})}^{x} - 3$ .

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

Short Answer

Step by step solution

Step 1. Using given information.

Step 2. Finding exponential function.

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

Short Answer

Step by step solution

Step 1. Using given information.

Step 2. Finding exponential function.

One App. One Place for Learning.

Most popular questions from this chapter

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Pure Maths

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Study anywhere. Anytime. Across all devices.

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