1a) Sketch the graph of f(x) = -2 (x+1)^3 (x-2)^2 using zeros, y-intercept, and end behaviour. Label all important points. b) A cubic function has three distinct x-intercepts at x= -1, 6, 2 and passes through the point (– 4, 15). Determine an equation to represent the function. c) Solve the following rational inequality. State your answer in set or interval notation. (x-4)(x+1) / x-3 > 0 d) Determine an equation of a rational function that has the following characteristics. a horizontal asymptote defined by y = 1 a vertical asymptote defined by x = − 2 a zero x = 4
1a) Sketch the graph of f(x) = -2 (x+1)^3 (x-2)^2 using zeros, y-intercept, and end behaviour. Label all important points. b) A cubic function has three distinct x-intercepts at x= -1, 6, 2 and passes through the point (– 4, 15). Determine an equation to represent the function. c) Solve the following rational inequality. State your answer in set or interval notation. (x-4)(x+1) / x-3 > 0 d) Determine an equation of a rational function that has the following characteristics. a horizontal asymptote defined by y = 1 a vertical asymptote defined by x = − 2 a zero x = 4
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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1a) Sketch the graph of f(x) = -2 (x+1)^3 (x-2)^2 using zeros, y-intercept, and end behaviour. Label all important points.
b) A cubic function has three distinct x-intercepts at x= -1, 6, 2 and passes through the point (– 4, 15). Determine an equation to represent the function.
c) Solve the following rational inequality. State your answer in set or interval notation. (x-4)(x+1) / x-3 > 0
d) Determine an equation of a rational function that has the following characteristics.
- a horizontal asymptote defined by y = 1
- a vertical asymptote defined by x = − 2
- a zero x = 4
These are all included in one question, please solve all with all work
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