For each equation, (a) give a table with at least three ordere...

Question

For each equation, (a) give a table with at least three ordered pairs that are solutions, and (b) graph the equation. See Examples 3 and 4.

y = |x - 2|

Accepted Answer

Welcome back everyone. In this problem, we want to sketch the graph of the equation Y equals the absolute value of X minus 15. By using a table of ordered pairs, we have two possible grids that we can sketch our graph on where the first grid has larger Y values. While the second grid has larger X values. Now we're working with the absolute value of an equation and recall that for a function for which we are finding its absolute value. So let's say that Y equals the absolute value of F FX. Then that means it will only return positive values for our function. So in other words, if we have our coordinate grid X and Y, then our graph will probably look something like this. Whenever the Y value start to become negative, it will return a positive value instead. So the idea here is that we are going to plot on our graph at least three points just to show the general direction of our graph. Because notice this function is a linear function. This is a so it would make it would form a line which we can use. OK. No, because where our function is X minus 15. That means the highest possible values of Y we'd probably need would be 15. So since we need at Y to be at le or at most equal to 15, we can use our graph with the larger X values. So let's go ahead and do that. So first or are we gonna figure out the three points we need, let's first start at the vertex of our absolute value equation. No notice that at the vertex, Y will be equal to zero because that's the least possible value of Y. So at the vertex, OK, Y equals zero. So that means the absolute value of X minus equals zero. In that case, that means that X must be equal to 15 because if X is 15, 15 minus 15 equals zero. So since X is 15 and Y equals zero, our vertex would be at the 0.15 0. OK? So that's our first point. Next, we need a point at which uh on the, on the left side of the vertex. OK? So let's use it when X equals zero. OK. So when X equals zero, then we can get some Y value on the Y axis. So when X equals zero, that means Y equals the absolute value of zero minus 15, which is the absolute value of negative 16, which is positive 15. So 0 15 is another point on our graph. So let's put 0 15, 11, 12, 13. 14 15 right there. Finally, we need a point on the right side of the vertex. So let's use when X is say 30 OK. So when X equals 30 again, you could have used any point that would fall on the right side. So any X value that would fall on the right side of our vertex when X equals 30 that means Y equals the absolute value of 30 minus 15, which equals the absolute value of 15, which means Y equals 15. So 30 15 is another point on our graph and 15 would fall right there. Know that we have the vertex and two points on either side, we can go ahead and plot our graph. So our graph is going to go on the left, it's going to go in that direction and on the right, it's going to oops, I need a straight line here on the right, it's going to go in that direction and this would be our graph of Y equals the absolute value of X minus where our vertex is 15, 0 or 11 point on the right hand side would have been 30 15. And on the left hand side, one of the points would have been 0 15. Thanks a lot for watching everyone. I hope this video helped.

For each equation, (a) give a table with at least three ordered pairs that are solutions, and (b) graph the equation. See Examples 3 and 4.
y = |x - 2|

Key Concepts

Absolute Value Function

Creating Ordered Pairs from an Equation

Graphing Piecewise Functions

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