To graph the desired function, we will make a table of values. To do so, we will assign some values to the x-variable and calculate the corresponding values for y.
x | ∣∣∣∣∣31x+1∣∣∣∣∣ | f(x)=∣∣∣∣∣31x+1∣∣∣∣∣ |
---|---|---|
-12 | ∣∣∣∣∣31(-12)+1∣∣∣∣∣ | 3 |
-9 | ∣∣∣∣∣31(-9)+1∣∣∣∣∣ | 2 |
-6 | ∣∣∣∣∣31(-6)+1∣∣∣∣∣ | 1 |
-3 | ∣∣∣∣∣31(-3)+1∣∣∣∣∣ | 0 |
0 | ∣∣∣∣∣31(0)+1∣∣∣∣∣ | 1 |
3 | ∣∣∣∣∣31(3)+1∣∣∣∣∣ | 2 |
Now, we will plot and connect the obtained points on a coordinate plane. Recall that the graph of an absolute value function has a V
shape.
We see above that the x-variable can take any value. We also see that y takes values that are greater than or equal to 0. With this in mind, we can write the domain and range of the function. Domain:Range: all real numbers y≥0