How to graph a function and its inverse? (Step-by-Step)

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The first thing you need to know is that the function and its inverse will be symmetric around the line y=x.

When we have the form

y=mx+b

1.- You need first to find the y-intercept which is going to be the independent value or b.

2.- Next we are going to use the rise/run. If you have a function with a value of ¾x, your rise will be of 3 and your run of 4. So you are going to move 3 units in the y-axis and then I move 4 units in the x-axis. And then graph that point

3. Now you're going to have two points that you will need to join forming a line

4. It's time for the inverse, we will do the same but now with the equation of the inverse.

5. Graph the line (try to use another color so that you can distinguish them)

6. Let's graph our line y=x, also called identity line. That will be a dash line where it's y-intercept is zero and has a slope of 1/1

7. If they seem they're reflected to each other, you do it right!

Easy right? Now let's learn how to graph a parabola and its inverse

Now the function will be expressed as something like this

y=ax^2+c

1.- First we need to find the vertex. When x is alone the value of it will be zero, the same happens with the y, if you don't have a constant then its value will be zero.

Important: is there is no negative sign before the a, the parabola will be opening upwards and if it does have a negative sign it will be opening downwards.

2.- Then you will substitute with any number you want in x. Example:

y=-x^2-2

And you decide to use -1 what you will do is the following. (-1)^2=1, in this case our vertex will be at (0,-2) and now you substitute in the -2. Now join the two dots and draw the parabola

3.- Draw your identity line at y=x

4. Now imagine you're placing a mirror in the identity line, how does the parabola look like? Now draw it in the graph