Graph f(x)=lx-3l and x=3 on the same set of coordinate axes. Write a description of the relationship between the two graphs.

i graphed absolute value of x-3
but how do you graph x=3

Since you have no y, you'll use the point (-3,0) and then draw a straight vertical line through this point. Anytime you have x = something, it will result in a vertical line through that point on the x-axis. Whenever you have y = something, it will result in a horizontal line through that point on the y-axis. For some reason, calculators appear to not accept x=, so you just have to do it by hand.

Oh wait, I meant graph (3,0) and draw a verticle line. Whoops!

To graph f(x) = |x - 3| and x = 3 on the same set of coordinate axes, you will first need to understand how to graph the two individual functions.

1. Graphing f(x) = |x - 3|:
- Start by choosing some x-values to plug into the function. For simplicity, you can use x = -3, -2, -1, 0, 1, 2, 3, 4, and so on.
- Calculate the corresponding y-values by substituting the chosen x-values into the function. For example, if x = 2, then |2 - 3| = |-1| = 1, so the point (2, 1) would be on the graph.
- Plot all the points you obtained from the calculations on the graph. Remember that the absolute value function will only give non-negative output, so the graph will be above or on the x-axis.
- Connect the plotted points with a smooth curve. The resulting graph should resemble a "V" shape, centered around x = 3.

2. Graphing x = 3:
- This equation represents a vertical line passing through x = 3.
- To graph it, simply draw a vertical line passing through the x-coordinate 3 on the graph. The line should extend indefinitely in both the positive and negative y-directions.

Now, observing the relationship between the two graphs:
- The graph of f(x) = |x - 3| is a "V" shape centered at x = 3, with the vertex of the "V" at (3, 0).
- The graph of x = 3 is simply a vertical line and does not change based on y-values.
- Hence, the two graphs intersect at the point (3, 0), which is the vertex of the absolute value function f(x) = |x - 3|.

Overall, the relationship between the two graphs is that they intersect at the point (3, 0) and do not intersect at any other point.