x- intercept:Let’s find the x- intercept of our new rational function q(x)!

q(x) = 19x + 550 7x + 337

In order to determine the x- intercept, set y = 0, because the x- intercept will take place at y = 0.

0 = 19x + 550 7x + 337

By setting up a proportion, we get the following:

0 = 19x + 5501 7x + 337

Cross multiplying gives us:

0 = 19x + 550

x = -28.9

Now let’s try it for some other ratios:

r(x) = 17x + 806 7x + 337Ratio of Asian

Students to Chicana Students

s(x) = -3x + 143 7x + 337

Ratio of Afro Am students to Chicana

Students

y- intercept:Let’s find the y- intercept of our new rational function q(x)!

q(x) = 19x + 550 7x + 337

In order to determine the y- intercept, set x = 0, because the x- intercept will take place at x = 0.

q(0) = 19(0) + 550 7(0) + 337

q(0) = 550 337

q(0) = 1.63

Given the statistics that our numbers are based on, what does this q(0) = 1.63 represent?

Now let’s try it for some other ratios:

r(x) = 17x + 806 7x + 337Ratio of Asian

Students to Chicana Students

s(x) = -3x + 143 7x + 337

Ratio of Afro Am students to Chicana

Students

Vertical Asymptote:Let’s find the vertical asymptote of our new rational function q(x)!

q(x) = 19x + 550 7x + 337

In order to determine the vertical asymptote, set the denominator = 0, then solve for x. The reason that this creates the vertical asymptote is because our rational function cannot have a denominator which equals zero (fractions can’t have zero in the denominator!).

7x + 337 = 0x = -48.1

Given the statistics that our numbers are based on, what does this x = -48.1 represent?

Now let’s try it for some other ratios:

r(x) = 17x + 806 7x + 337Ratio of Asian

Students to Chicana Students

s(x) = -3x + 143 7x + 337

Ratio of Afro Am students to Chicana

Students

Domain (only try AFTER Vertical Asymptote):Let’s find the domain of our new rational function q(x)!

q(x) = 19x + 550 7x + 337

Because we know that domain are all the possible INPUT values for a function, the domain strictly consists of the possible input values for x. Let’s go back to the vertical asymptote we obtained earlier: x ≈ -48.1 (approximately). If we plug this value into the equation, we will get an

undefined value for q(x).

q(-48.1) ≈ 19(-48.1) + 550 7(-48.1) + 337

≈ -363.9 0

Does that work? No. So -48.1 is not allowed to be one of our input values… So our domain (our input values) can only run from -∞ < x<-41.8, and from -41.8< x < ∞. Let’s re- write this in the proper form:

(-∞ ,-41.8) U (-41.8, ∞)

This way, the only point not included in our domain is x = -41.8 (our vertical asymptote)

r(x) = 17x + 806 7x + 337Ratio of Asian

Students to Chicana Students

s(x) = -3x + 143 7x + 337

Ratio of Afro Am students to Chicana

Students

Horizontal Asymptote:Let’s find the horizontal asymptote of our new rational function q(x)!

q(x) = 19x + 550 7x + 337

In order to determine the horizontal asymptote, we will divide both the numerator and denominator by the highest power of x in the function. It does not matter whether the highest power of x is in the numerator or denominator– just take the highest power of x.

For our function, the highest order of x is x1, so we will divide both the numerator and denominator by x1

19x + 550 x

7x + 337 x

19x/x + 550/x

7x/x + 337/x

19 + 550/x

7 + 337/x

What happens as x approaches infinity? The two smaller fractions get increasingly small to the point where they become negligible (insignificant). At that point, we are left with the fraction 19/7 or approximately 2.7 which is our horizontal asymptote. Try it for the two

functions below!r(x) = 17x + 806 7x + 337

Ratio of Asian Students to Chicana Students

s(x) = -3x + 143 7x + 337

Ratio of Afro Am students to Chicana Students