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Chapter 5: Q. 100 (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)=-e-xifx<0-exifx鈮�0

Short Answer

Expert verified

The graph of the given function

The domain of the given function (-鈭�,鈭�) The range of the given function (-鈭�,-1)

The graph never touches the x-axis, there is no x-intercept.

y-intercepts (0,-1)

Step by step solution

01

Step 1.Given information

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

02

Step 2.Finding the x and y values for f(x)=-e-x

Let us begin with the graph of f(x)or y=-e-x Since this function is defined for the value of x less than zero, select some values for x that are less than 0 and find the corresponding values of y

Create a table using the values.

x y = -e-x
-1 -2.178
-32 -4.482
-2 -7.389
03

Step 3.Finding the x and y values for f(x)=-ex

Similarly, for the function y=-ex, select some values for x that are greater than or equal to 0 .
xy = -ex
0 -1
1 -2.718
2 -7.389
04

Step 4.Plot the points for the two functions. Connect each set of points using a smooth curve.

The domain of a function is the set of allx-values for which the function is defined. We can see thatf(x)is defined for all real numbers. The domain off(x)is the interval(-鈭�,鈭�).
The range is the set of values of the function. From the graph, it is possible to say that the range off(x)is the interval(-鈭�,-1).
The y-intercept is(0,-1) . Since the graph never touches the x-axis, there is no x-intercept.

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Most popular questions from this chapter

Answers are given at the end of these exercises. If you get a wrong answer, read the pages listed in red.

For an exponential function, f(x)=Cax,f(x+1)f(x)=

A function y=f(x)is increasing on the interval (0,5).What conclusions can you draw about the graph of y=f-1(x)?

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

fx=ex-1

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

9-x+15=27x

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
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