Homework 1 Math 22 - College Algebra PDF

Math 22 - College Algebra with Analytic Geometry and Applications II Homework 1 Instructions: Full Solutions to these problems must be uploaded to Canvas before the deadline. Solutions must be organized, legible, and all papers mu...

Math 22 - College Algebra with Analytic Geometry and Applications II Homework 1 Instructions: Full Solutions to these problems must be uploaded to Canvas before the deadline. Solutions must be organized, legible, and all papers must be stapled. Points will be deducted for incomplete reasoning and disorganized work, even if your answers are correct. No late submissions will be accepted. Problem 1: Complete the following for the given function f (x). (a) Find f (x + h) and fully simplify your result. (b) Find the difference quotient of f and fully simplify your result. a. f (x) = 5 b. f (x) = 3x + 2 c. f (x) = 11 − 6x Problem 2: Let f (x) = 2x2 − 5x + 1. a. Find f (x + h) and fully simplify your answer (fully expand the expression). f (x + h) − f (x) b. Find the difference quotient and fully simplify your answer (meaning, simplify h and eliminate h). Problem 3: Let g(z) = 17 − 3z 2. a. Find g(z + h) and fully simplify your answer (fully expand the expression). g(z + h) − g(z) b. Find the difference quotient and fully simplify your answer (meaning, simplify h and eliminate h). Problem 4: Epidemiologists in a particular town estimate that t days after the flu begins to spread in the town, the percent of the population infected by the flu is approximated by p(t) = t2 + t, for 0 ≤ t ≤ 5. a. Evaluate p(1) and interpret what it means. Also, be sure to include the units. p(t + h) − p(t) b. Find the difference quotient and fully simplify your answer. h c. Evaluate the difference quotient when t = 4 and h = 0.05. Interpret your result and include units. Problem 5: Let the distance in feet that an object travels in t seconds be given by d(t) = 7t2 for 0 ≤ t ≤ 10. a. Evaluate d(2) and interpret its meaning. Also, be sure to include the units. b. Find d(t + h) and fully simplify your answer (fully expand the expression). d(t + h) − d(t) c. Find the difference quotient and fully simplify your answer h d. Evaluate the difference quotient when t = 2 and h = 0.03 and include appropriate units. e. Use your answer from part (e) and interpret its meaning. Page 1 of 1