x- intercept:

1. 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 + 550 1 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 + 337 Ratio of Asian Students to Chicana Students s(x) = -3x + 143 7x + 337 Ratio of Afro Am students to Chicana Students

2. 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 + 337 Ratio of Asian Students to Chicana Students s(x) = -3x + 143 7x + 337 Ratio of Afro Am students to Chicana Students

3. 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 = 0 x = -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 + 337 Ratio of Asian Students to Chicana Students s(x) = -3x + 143 7x + 337 Ratio of Afro Am students to Chicana Students

4. 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) s(x) = -3x + 143 7x + 337 Ratio of Afro Am students to Chicana Students r(x) = 17x + 806 7x + 337 Ratio of Asian Students to Chicana Students

5. 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! s(x) = -3x + 143 7x + 337 Ratio of Afro Am students to Chicana Students r(x) = 17x + 806 7x + 337 Ratio of Asian Students to Chicana Students