Learning Objectives:

__Graphing Functions____ __

A **function**** ****(**a set of** ****ordered pair)** is a special relationship where each input has a single output. While **graphing**, if we're not sure what the **function** looks like we can always go back to making a table of values and notice how all the **functions** will be given using **function** notation, as well as replacing **(f of x)** with **y**. We **graph functions** in exactly the same way that we **graph equations**. If we know ahead of time what the **function** is a **graph** of we can use that information to help us with the **graph** and if we don’t know what the **function** is ahead of time then all we need to do is plug in some **x’s **compute the value of the **function (**which is really a **y** value**)** and then plot the points. In order to **graph a linear equation** we work in **3 steps:** **First** we solve the equation for **y.**

**Second** we make a table for our **x- and y-values**. From the **x values** we determine our **y-values.**

**Last** we graph our matching **x- and y-values** and draw a line. Therefore the graph of a function** f** is the set of all points in the plane of the form **(x, f(x)). **We could also define the **graph of f** to be the **graph** of the equation **y = f(x).**

**Hook Questions**

*1. **How do you graph a quadratic equation?*

*2. **How do you graph a rational function?*

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