To graph the given piecewise function, we should think about the graph of each individual piece of the function. Then we can combine the graphs on one coordinate plane.
f(x)=2^x
First we will graph f(x)=2^x for the domain x≥ 0. Notice that this is an exponential function.
f(x)= 2^x
Because the base of the function is greater than 1, we know that this is an exponential growth function. To draw the graph we will start by making a table of values. Remember that all of x-values need to be greater than or equal to 0.
x
2^x
f(x)=2^x
0
2^0
1
1
2^1
2
2
2^2
4
3
2^3
8
The ordered pairs ( 0, 1), ( 1, 2), ( 2, 4), and ( 3, 8) all lie on the graph of the function. Now, we will plot and connect these points with a smooth curve. Remember that since the endpoint is included, this piece should end with a closed circle.
f(x)=|x|
Next, we will graph f(x)=|x| for the domain x<0. To draw the graph we will start by making a table of values. Remember that all x-values need to be less than 0.
x
|x|
f(x)=|x|
- 1
| - 1|
1
- 3
| - 3|
3
- 5
| - 5|
5
The ordered pairs ( - 1, 1), ( - 3, 3), and ( - 5, 5) all lie on the graph of the function. Now, we will plot and connect these points with a line. Remember that since the endpoint is not included, we will end the piece with an open circle.
Combining the Pieces
Finally, we can combine the pieces onto one coordinate plane.
