Solving Rational Expressions and Graphs Review

The video tutorial provides a step-by-step guide on graphing rational functions. It covers finding x and y intercepts, identifying vertical and horizontal asymptotes, and determining the domain and range. The tutorial includes two example problems, each demonstrating the process of graphing a rational function and interpreting its characteristics.

What is the first step in graphing a rational function?

• Find the y-intercept

• Find the x-intercept

• Determine the domain

• Find the vertical asymptote

How do you find the x-intercept of the function f(x) = 4/(x-3)?

• Set the denominator equal to zero

• Set y equal to zero

• Set the numerator equal to zero

• Set x equal to zero

What is the y-intercept of the function f(x) = 4/(x-3)?

• 4

• 1 and 1/3

• -4

• -1 and 1/3

What is the vertical asymptote of the function f(x) = 4/(x-3)?

• x = 0

• x = 3

• y = 0

• y = 3

What is the horizontal asymptote of the function f(x) = 4/(x-3)?

• y = 0

• x = 3

• y = 3

• x = 0

What is the domain of the function f(x) = 4/(x-3)?

• (-∞, 4) ∪ (4, ∞)

• (-∞, 0) ∪ (0, ∞)

• (-∞, -3) ∪ (-3, ∞)

• (-∞, 3) ∪ (3, ∞)

How do you find the x-intercept of the function (6x+1)/(2x-4)?

• Set y equal to zero

• Set the numerator equal to zero

• Set the denominator equal to zero

• Set x equal to zero

What is the y-intercept of the function (6x+1)/(2x-4)?

• 1

• 1/4

• -1/4

• -1

What is the vertical asymptote of the function (6x+1)/(2x-4)?

• y = 2

• y = 0

• x = 2

• x = 0

What is the horizontal asymptote of the function (6x+1)/(2x-4)?

• y = 3

• y = 0

• x = 3

• x = 0