Ayyoo kids! Today, Joe and I are going to explain what Rational Functions are!

Yeah, it's what all the big kids say in the neighborhood, so you gotta learn the lingo dawg...BAHAAHAH YOU'RE A DOG

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Here's are a few examples of how they Rational Functions look like!

This one's my favorite for no apparent reason...

Now that you know what they look like, a rational function is any function that is in the form of x: (k/x) where k is a constant. It is a unique rational function called a reciprocal function. It is essentially a function that's the ratio of two polynomials. Here are a few characteristics to consider:

1. The graph of these functions will always look like a rectangular hyperbola (like a two hugeee curves) and will be symmetrical about the diagonal lines y=x and y=-x

2. The value of k also impacts the function's concavity and location. If k increases the concavity decreases, and if k decreases, the concavity increases!

3. To continue, any point on the graph where f(x)=0, the function (1/f(x)) will not exist. And, we can show this by drawing a dashed line, which is called an asymptote!

4. These graphs also have horizontal asymptotes.

Now, you might be wondering how you can graph one of those cool functions we saw earlier. Lemme show you how it's done!

Graphing a Rational Function

1. Simplify the function...always!

2. Find the x-intercepts by making the numerator equal to 0.

3. Then, find the vertical asymptotes by setting the denominator equal to 0.

Graphing a Rational Function

1. Simplify the function...always!

2. Find the x-intercepts by making the numerator equal to 0.

3. Then, find the vertical asymptotes by setting the denominator equal to 0.

Graphing a Rational Function Pt.2

4. Then, find the horizontal asymptotes...but there's a process. 

Given that f(x)=p(x)/q(x)

If the...

    a. degree of p is > than the degree of q → no horizontal asymptote 

    b. degree of p is < than the degree of q→xaxis/y=0

     c. degree of p = degree of q →coefficient of p(x) over coefficient of q(x)

Graphing a Rational Function Pt.3

5. Find the holes in the function which only occurs WHEN there's a common factor between the numerator and denominator. 

And if you're still a noob and need help...

    a. To find the x coordinate: set the common factor to 0.

    b. To find the y coordinate: substitute the x coordinate into the simplified function.