MATH 32 Study Guide - Midterm Guide: Even And Odd Functions, Asymptote, Inverse Function

• School: Berkeley
• Department: Mathematics
• Course: MATH 32
• Professor: All

Document Summary

Solution: g(x) = 2f (x + 3) = 2 x + 3 (2) (6 points) give an example of a rational function with a horizontal asymptote at y = 0 and a vertical asymptote at x = 1. A rational function is of the form p(x) q(x) To ensure a horizontal asymptote at y = 0, the degree of p should be less than the degree of q. To ensure a vertical asymptote at x = 1, 1 should be a zero of q(x), but not a zero of p(x). 1 x + 1 x2 x3 + 1 x + 7 x(x + 1) (3) (12 points) let h(x) = 2x2 12x + 5. To nd the range, let"s think about the graph of h(x). It is a parabola, convex up (since the coe cient of x2 is 2 > 0). The minimum output value is the y-coordinate of the vertex. = 2((x 3)2 9) + 5.