Unit 3 rational functions lesson 8 rational functions unit test answers
As an AI language model, I don't have access to your specific test answers. However, here are a few practice questions and answers to help you prepare for your rational functions unit test:
1) What is the domain of the function f(x) = (x-3)/(x+2)?
Answer: The denominator cannot equal zero, so x+2 cannot equal zero. Solving for x, we get x ≠ -2. Therefore, the domain is all real numbers except for x=-2.
2) What are the vertical asymptotes of the function g(x) = 4/(x-1)^2 ?
Answer: The denominator cannot equal zero, so x-1 cannot equal zero. Solving for x, we get x ≠ 1. Therefore, the vertical asymptote is x=1.
3) Find the x-intercept(s) of the function h(x) = (2x-1)/(x^2-4x+3).
Answer: To find the x-intercept(s), we set y=0 and solve for x. Therefore, we solve the equation (2x-1)/(x^2-4x+3) = 0:
2x-1=0 or x^2-4x+3=0
Solving for x, we get: x=1/2 or x=1 or x=3. Therefore, the x-intercepts are (1/2, 0), (1, 0), and (3, 0).
4) Find the horizontal asymptote of the function f(x) = (3x^2-2)/(2x^2+5x+6).
Answer: To find the horizontal asymptote, we examine the highest degree terms in the numerator and denominator. In this case, both the numerator and denominator have degree 2, so we divide the leading coefficients: 3/2. Therefore, the horizontal asymptote is y=3/2.
5) Simplify the expression: (x^2 + 2x - 8)/(x^2 - 4)
Answer: To simplify, we factor the numerator and the denominator:
(x^2 + 2x - 8) = (x+4)(x-2)
(x^2 - 4) = (x+2)(x-2)
Therefore, the expression simplifies to: (x+4)/(x+2).