If I have an equation, q(x) = x, and I have to identify what the graph of that would look like, isn't it just going to be a straight line?
There are two straight lines to choose from -- one is horizontal across the x-axis on the 1, and the other is horizontal across the x-axis on the 2.
Which is correct?
Thank you.
The way you described the given graphs, neither one is correct
q(x) = x or y = x
is a straight line passing through the origin and forming a 45° with the x-axis
Verification:
http://www.wolframalpha.com/input/?i=plot+q(x)+%3D+x
To understand what the graph of the equation q(x) = x would look like, you can follow these steps:
Step 1: Plot some points.
- To start, choose a few different values for x and calculate the corresponding values for q(x). For example, let's choose x = -2, -1, 0, 1, and 2:
- q(-2) = -2
- q(-1) = -1
- q(0) = 0
- q(1) = 1
- q(2) = 2
Step 2: Plot the points on a coordinate axis.
- On a graph with an x-axis and a y-axis, plot the points you calculated in step 1. So, for example, at x = -2, y = -2, so you would plot the point (-2, -2). Similarly, for x = -1, y = -1, so you would plot the point (-1, -1), and so on.
Step 3: Connect the points.
- Once you have plotted all the points, it's time to connect them. Since the equation q(x) = x is a straight line equation, you will find that the plotted points lie on a straight line.
From your description, it seems that you are considering two options for the graph - a horizontal line across the x-axis at 1 and another at 2. However, if you plot the points as described above, you will find that neither of these options is correct.
The graph of q(x) = x will be a diagonal line that passes through the origin (0,0) and has a slope of 1. This means that for every unit you move along the x-axis, the corresponding point on the graph will move up by one unit on the y-axis.
Therefore, the correct graph for the equation q(x) = x is a straight line that starts at the origin (0,0) and goes through all the points you plotted.
I hope this explanation helps you understand how to graph the equation q(x) = x!