Problem Solving > Sketch the Graph on the Cartesian Plane

Let’s say you were given a function like f(x) = x^{2} – 2 (or, equivalently, y = x^{2} – 2) and** asked to sketch the graph on the Cartesian Plane**. In order to solve the problem you need to:

- Choose your x-values to input into the formula. Usually you’ll want to choose integers (whole numbers plus zero and negatives like -10, 3, 1, 7…) because they are easier to work with.
- Create a few (x, y) coordinates.
- Plot the points on a Cartesian plane (also called an x-y graph).
- Draw the curve or line of the graph.

## Sketch the Graph on the Cartesian Plane: Example

**Example question #1:** Sketch the graph of y = x^{2} – 2 on the Cartesian plane.

Step 1: **Choose your x-values**. It’s up to you what values to choose for your x-values, but pick numbers that are easy to calculate. A good starting point is a few values around zero: -2, -1, 0, -1, 2. Or you could try -10, -5, 0, 5, 10.

Step 2: **Input your x-values from Step 1 into the function.** To do this, you replace the “x” in the formula with the number you choose for x. Let’s use -2, -1, 0, -1, 2.

- y = x
^{-2}– 2 = 2 - y = x
^{-1}– 2 = -1 - y = x
^{0}– 2 = -2 - y = x
^{1}– 2 = -1 - y = x
^{2}– 2 = 2

Step 3: **Create a table of values **from Steps 1 and 2. This step is optional, but it can help you see the (x, y) points a little more clearly:

Step 4: **Plot the points.**

Step 5: **Draw the curve or line of the graph. **This is really just connecting the dots.

If you aren’t sure at this point about the shape of the graph, go back to Step 1 and choose a couple more x-values to complete the picture.

Step 6: Check your work. You could use a graphing calculator: I used the one at Desmos.com to create the graphs here.

If you can’t use a graphing calculator, throw in a random x-value as an input, like x = 9.2 or x = 7.5. If you have drawn your graph correctly, your new point will fall on the line you drew.

**Tip**: Unless you have a linear function, which always gives a straight line graph, draw a curve from each point to the next instead of a series of straight lines. For example,** don’t do this:**

**CITE THIS AS:**

**Stephanie Glen**. "Sketch the Graph on the Cartesian Plane" From

**CalculusHowTo.com**: Calculus for the rest of us! https://www.calculushowto.com/sketch-the-graph-on-the-cartesian-plane/

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