x- intercept: Let’s find the x- intercept of our new rational function q(x)! q(x) = 19x x In order to determine the x- intercept, set y = 0, because the x- intercept will take place at y = 0. 0 = 19x x By setting up a proportion, we get the following: 0 = 19x x Cross multiplying gives us: 0 = 19x x = Now let’s try it for some other ratios: r(x) = 17x x Ratio of Asian Students to Chicana Students s(x) = -3x x 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 x In order to determine the y- intercept, set x = 0, because the x- intercept will take place at x = 0. q(0) = 19(0) (0) q(0) = 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 x Ratio of Asian Students to Chicana Students s(x) = -3x x 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 x 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 = 0 x = Given the statistics that our numbers are based on, what does this x = represent? Now let’s try it for some other ratios: r(x) = 17x x Ratio of Asian Students to Chicana Students s(x) = -3x x 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 x 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 ≈ (approximately). If we plug this value into the equation, we will get an undefined value for q(x). q(-48.1) ≈ 19(-48.1) (-48.1) ≈ Does that work? No. So 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 = (our vertical asymptote) r(x) = 17x x Ratio of Asian Students to Chicana Students s(x) = -3x x 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 x 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 x 1, so we will divide both the numerator and denominator by x 1 19x x 7x x 19x / x / x 7x / x /x / x /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 x Ratio of Asian Students to Chicana Students s(x) = -3x x Ratio of Afro Am students to Chicana Students