Graph it

Graphing a function is the easy part, assuming you know how to plot points on a graph. Click here to practice plotting points.

Now that you remember how to plot points, let's figure out how to graph our familiar function f(x) = 2x+1.

In order to graph a function, we need ordered pairs. We can make ordered pairs by evaluating the function at given values. For instance, remember when we evaluated this function at x = 5? The input was 5 and the output was 11. We can easily turn this into the ordered pair (5, 11) and graph it. But wait, this only gives us one point, and we need at least two points to make a line!

Pick a few other values for x (if you're smart, you'll pick small numbers that are easy to plug in), and evaluate them as well. I picked 0, 1, and 2. Organize your ordered pairs into a table like you see below.

f(x) = 2x+1 f(x) = 2(x)+1 f(x) = 2(x)+1 f(x) = 2(x)+1

f(0) = 2(0)+1 f(1) = 2(1)+1 f(2) = 2(2)+1 f(5) = 2(5)+1

f(0) = 0+1 f(1) = 2+1 f(2) = 4+1 f(5) = 10+1

f(0) = 1 f(1) = 3 f(2) = 5 f(5) = 11

Now all you've got to do is plot those points and connect the dots. It should look like this:

*Note: Eventually, we will examine cases where we should not connect the dots.