Homework

Problem 1 · easy

Find the domain of f(x) = 3/(x - 7).

Problem 2 · easy

Find the domain of g(x) = (x + 1)/((x - 2)(x + 5)).

Problem 3 · easy

Find the vertical asymptote(s) of f(x) = 4/(x^2 - 16).

Problem 4 · medium

Does f(x) = (x - 3)/(x^2 - 9) have a hole or a vertical asymptote at x = 3?

Problem 5 · medium

What is the y-value of the hole in f(x) = (x - 3)/(x^2 - 9)?

Problem 6 · easy

Find the horizontal asymptote of f(x) = (5x^2 - 1)/(x^2 + 3).

Problem 7 · easy

Find the horizontal asymptote of f(x) = (2x + 1)/(x^3 - 4).

Problem 8 · medium

Does f(x) = (x^3 + 2)/(x - 1) have a horizontal asymptote?

Problem 9 · medium

Find the slant asymptote of f(x) = (x^2 + 2x + 3)/(x + 1).

Problem 10 · easy

Find the x-intercept(s) of f(x) = (x^2 - 1)/(x + 3).

Problem 11 · easy

Find the y-intercept of f(x) = (x - 2)/(x + 4).

Problem 12 · medium

On which intervals is f(x) = (x - 1)/(x + 3) positive?

Problem 13 · medium

Solve: 2/(x + 1) = 3/x. Find x.

Problem 14 · challenge

Solve: 1/(x - 2) + 1/(x + 2) = 4/(x^2 - 4).

Problem 15 · medium

Find all asymptotes of f(x) = (3x)/((x-1)(x+2)).

Problem 16 · challenge

Is there a hole in f(x) = (x^2 - 4x)/(x^2 - 16)? If so, where?

Problem 17 · medium

Find the VA of f(x) = x/(x^2 - x - 6).

Problem 18 · challenge

Solve: x/(x - 3) = 9/(x - 3) + 2.

Problem 19 · medium

What is the HA of f(x) = (7x^3 - 2)/(4x^3 + 1)?

Problem 20 · medium

Does f(x) = (x^2 - x - 6)/(x - 3) have a hole? Where is it, and what is the y-value?

Problem 21 · easy

Find all zeros of f(x) = (x^2 - 9)/(x - 1).

Problem 22 · medium

For f(x) = 1/(x^2 + 1), state the domain and HA.

Problem 23 · challenge

Solve: 3/(x+2) - 1/(x-2) = 2/(x^2-4).

Problem 24 · medium

Sketch description: what does f(x) = 1/(x-1)^2 look like near x = 1?

Problem 25 · medium

A population model is P(t) = 1000t/(t + 10). What does P approach as t goes to infinity?