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Chapter 5: Q. 86 (page 284)

In Problems $85 - 88$ , determine the exponential function whose graph is given.

Short Answer

Expert verified

The exponential function obtained is $f (x) = 5^{x}$ .

Step by step solution

01

Step 1. Given information

Given graph of exponential function is

The graph passes through $(- 1, \frac{1}{5}), (0, 1), (1, 5)$ .

02

Step 2. Finding exponential function.

Assume that the graph follows the function $f (x) = a^{x}$

which gives

$5 = a^{1} 5 = a$

So the exponential function is $f (x) = 5^{x}$ .

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Most popular questions from this chapter

Height and Head Circumference. The head circumference

C of a child is related to the height H of the child (both in inches) through the function $H (C) = 2.15 C - 10.53$

(a) Express the head circumference C as a function of height H.

(b) Verify that $C = C (H)$ is the inverse of $H = H (C)$ by showing that $H (C (H)) = H$ and $C (H (C)) = C$ .

(c) Predict the head circumference of a child who is $26$ inches tall.

Solve the equation $3^{x^{3}} = 9^{x}$

and verify your results using a graphing utility.

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

If $g (- 5) = 3$ and g is one-to-one, what is $g^{- 1} (3)$ ?

Solve the equation $5^{x} = 5^{- 6}$

and verify your results using a graphing utility

See all solutions

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