Graph the functions in Exercises 37–56.

y = |...

Question

Graph the functions in Exercises 37–56.

y = |x − 2|

Accepted Answer

Hi everyone, let's take a look at this practice problem. This problem says for the given function, draw the graph, and we're given the function Y is equal to the absolute value of the quantity of X minus 21 in quantity. And below the problem we're given a graph on which to plot our function. So this problem we just need to draw the graph of Y is equal to the absolute value of the quantity of X minus 21 in quantity. So, we're actually going to draw this graph using transforms. So, we're going to begin by looking at the function Y is equal to the absolute value of X. I recall that this gives us a V-shape graph with a vertex at the origins, so we have a vertex. Of our V at the point 0.0. And we have a slope of one. When X is greater than 0 and a slope. Of -1. When X is less than 0. So now what we're going to do is look at the function that we're given, which is Y is equal to the absolute value of the quantity of X minus 21 in quantity. And we see here is that we've just shifted the X um origin to the right by 21 units. That means that we're going to have a vertex for our V shape. Located at the point of 21.0. And so that means that we're going to have a slope. Of one, When X is greater than 21 and will have a slope. Of -1. When X is less than 21. So now we're going to use this information to actually draw our graph. So we'll start off by placing a point at our vertex. At 21.0. And now we need to draw two straight lines indicating um each side of our V shape for the absolute value function. And we can actually just pick two points, one on each side of our um value of X equal to 21. So we'll choose X equal to 41, and that will give us a Y value of 20. And the other value that we can choose to the left of X equals to 21 is gonna be X equal to 1, and that will give us also a Y value of 20. So now all we need to do is connect our vertex through each of these points and extend it all the way to the edge of the graph. And so, if we do this for each side, we'll again get our classic V shape for the absolute value function. And so, the graph that we have drawn on the screen here is the answer to this problem. So, I hope that this explanation has been useful, and I'll see you in the next video.

Graph the functions in Exercises 37–56.

y = |x − 2|

Key Concepts

Absolute Value Function

Graphing Techniques

Vertex of a Function

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