Graph Absolute Value Functions
You might recall from Algebra 1 that an absolute value function has a v-shaped graph. A function in the form \(f\left(x\right)=a\left|x-h\right|+k\) has a vertex at \(\left(h,k\right)\). But what happens when a function has multiple absolute values within it? Go check out the investigation to find out what the graph of \(f\left(x\right)=\left|x\right|+\left|x-3\right|\) would look like.
We can graph an absolute value function in three ways. 1) With technology 2) By making a table of values and plotting specific coordinates, or 3) By understanding the pieces that make up a particular function, and graphing the pieces. In order to graph an absolute value function the third way, we'll find the turning points and then use a number line to figure out what is happening before, in between and after these turning points. See the example for step-by-step directions of how to do this.
Example 1: Graph \(f\left(x\right)=\left|x\right|+\left|x-3\right|\). You've seen how this graph looks in the investigation, we're now going to see how to graph it by hand.
You might recall from Algebra 1 that an absolute value function has a v-shaped graph. A function in the form \(f\left(x\right)=a\left|x-h\right|+k\) has a vertex at \(\left(h,k\right)\). But what happens when a function has multiple absolute values within it? Go check out the investigation to find out what the graph of \(f\left(x\right)=\left|x\right|+\left|x-3\right|\) would look like.
We can graph an absolute value function in three ways. 1) With technology 2) By making a table of values and plotting specific coordinates, or 3) By understanding the pieces that make up a particular function, and graphing the pieces. In order to graph an absolute value function the third way, we'll find the turning points and then use a number line to figure out what is happening before, in between and after these turning points. See the example for step-by-step directions of how to do this.
Example 1: Graph \(f\left(x\right)=\left|x\right|+\left|x-3\right|\). You've seen how this graph looks in the investigation, we're now going to see how to graph it by hand.