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Magazine Chapter 5: Q. 98 (page 285)
In Problems 97-100,graph each function,Based on the graph,state the domain and the range and find any intercepts.
Short Answer
Expert verified
Graph of the given function
Domain of the given function .
Range of the given function .
The y-intercept is . The two functions have the line as their horizontal asymptote. As the value of increases, becomes smaller and the graph will approach the line . But, it will not intersect the line. Similar is the case with the graph of also. This implies that there is no x-intercept.
Step by step solution
01
Step 1.Given information
The given function
02
Step 2.Finding the x and y values for f(x)=ex
Let us begin with the graph of or . Since this function is defined for the value of x less than zero, select some values for that are less than 0 and find the corresponding values of.
Create a table using the values.
| x | y=ex |
| -3 | 0 |
| -2 | 0.1 |
| -1 | 0.4 |
03
Step 3.Finding the x and y values for y=e-x
Similarly, for the function , select some values for x that are greater than or equal to 0 .
| x | y=e-x |
| 0 | 1 |
| 1 | 0.4 |
| 2 | 0.1 |
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 all x-values for which the function is defined. We can see that is defined for all real numbers. The domain of is the interval .
The range is the set of values of the function. From the graph, it is possible to say that the range of is the interval .
The y-intercept is . The two functions have the line as their horizontal asymptote. As the value of x increases, becomes smaller and the graph will approach the line . But, it will not intersect the line. Similar is the case with the graph of also. This implies that there is no x-intercept.
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