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Chapter 5: Q. 85 (page 284)

Determine the exponential function whose graph is given.

Short Answer

Expert verified

The exponential function isf(x)=3x.

Step by step solution

01

Step 1. Given Information

Points given on graph:

(-1,13),(1,3),(0,1),(2,9)

We have to find the exponential of the form f(x)=ax

where f(x+1)f(x)=a,a>0

and x is any real number.

02

Step 2. Calculating the ratios

Put x=0

f(x+1)f(x)=f(1)f(0)

From graph , we get , f(1)=3,f(0)=1

f(1)f(0)=31=3

Put x=1 ,

f(x+1)f(x)=f(2)f(1)

From graph , we get , f(2)=9,f(1)=3

f(2)f(1)=93=3

Similarly , we get , ratios for x=-1,x=2

The ratios for them is also 3.

03

Step 3. Getting the final exponential function 

Since the ratios calculated above is 3.

Therefore , a=3

Hence , the exponential function isf(x)=3x.

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Most popular questions from this chapter

The domain of one-to-one function g is0,15, and range is (0,8). State the domain and range oflocalid="1646180141229" g-1

In Problems 33-40, the graph of an exponential function is given. Match each graph to one of the following functions.

If f(x)=ax+band g(x)=cx+d, then find: -

(a)f鈭�g

(b)g鈭�f

(c)the domain of f鈭�gand g鈭�f

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In Problems 61鈥�72, the function f is one-to-one. Find its inverse and check your answer.

f(x)=2x3x-1

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

ex=e3x+8
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