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Chapter 5: Q. 99 (page 285)

In Problems 97-100,graph each function,Based on the graph,state the domain and the range and find any intercepts.

f(x)=-exifx<0-e-xifx鈮�0

Short Answer

Expert verified

Graph of the given function

The domain of the graph is the set of all real numbers or the interval(-鈭�,鈭�) . Sincef(x) is negative for any value ofx , the graph off(x) will never cross the x-axis. So, the range is the interval[1,0) . The only intercept is(0,-1) .

Step by step solution

01

Step 1.Given information

The given functionf(x)=-exifx<0-e-xifx鈮�0

02

Step 2.Draw graph for f(x)=-ex

The graph of f(x)=-ex for x<0 consits of onlybthe negtive values ofx.

03

Step 3.Draw graph for f(x)=-e-x

The graph of f(x)=-e-xfor x 鈮�0 consits of only the positive values of xincluding 0.

04

Step 4.Draw graph for both f(x)=-ex         if x<0-e-x       if  x≥0

The graph of f(x)=-exifx<0-e-xifx鈮�0will consits of both the graphs of f(x)=ex for x>0 and f(x)=-e-xfor x鈮�0

From the graph, we can say that the domain of the graph is the set of all real numbers or the interval (-鈭�,鈭�). Since f(x) is negative for any value of x , the graph of f(x) will never cross the x- axis. So, the range is the interval [-1,0). The only intercept is (0,-1).

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Most popular questions from this chapter

Solve given equation and verify your result using graphing utility.

ex2=e3x.1e2

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

(d)the conditions for whichf鈭�g=g鈭�f

Use the graph of y=f(x)given in the Problem 43to evaluate the following:

(a) f(-1)

(b) f(1)

(c) f-1(1)

(d) f-1(2)

Find f(3x)iff(x)=4-2x2.

If 3-x=2, what does32xequal ?
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