Practice Set 2
10 Connected Questions
This set focuses on matching graphs to equations, solving rational equations, and connecting restrictions to graph behavior.
Practice Questions
DOK 2 Practice Set: Rational Connections
Use Desmos to compare graphs, equations, and tables while you solve rational equations and explain function features.
Question 1
The graph shown has a vertical asymptote at x = 2 and a horizontal asymptote at y = 1. Which equation matches it best?
Match the vertical and horizontal asymptotes before choosing the equation.
Desmos Move: Use the asymptotes as anchors in Desmos. The graph should approach x = 2 vertically and y = 1 horizontally.
Question 2
Solve 2 / (x - 1) = 1.
Desmos Move: You can solve algebraically by multiplying both sides by x - 1, then confirm the intersection in Desmos.
Question 3
Which value is excluded from the domain of (x² - x - 6) / (x² - 9) after simplifying?
Desmos Move: Factor both numerator and denominator first. Even if a factor cancels, the original denominator still controls restrictions.
Question 4
Which statement correctly describes y = (x + 4) / (x - 1)?
Desmos Move: Use the numerator for the x-intercept, substitute x = 0 for the y-intercept, and set the denominator to 0 for the vertical asymptote.
Question 5
If (x² - 4x) / x = 5, what is the valid solution?
Desmos Move: Simplify carefully to x - 4, but keep the original restriction x ≠ 0 before you solve.
Question 6
Which graph feature shows a hole instead of a vertical asymptote?
Desmos Move: If the factor cancels, the graph usually follows the simplified rule except for one missing point.
Question 7
The table shows values of a rational function. Which value is most likely the vertical asymptote?
| x | 1.5 | 1.9 | 2.1 | 2.5 |
|---|---|---|---|---|
| f(x) | -6 | -30 | 30 | 6 |
Large outputs on both sides of the same x-value usually signal a vertical asymptote.
Desmos Move: When outputs become very large positive and negative near the same x-value, that x-value is usually a vertical asymptote.
Question 8
Which equation has a hole at x = -1 and a vertical asymptote at x = 3?
Desmos Move: A hole comes from a shared factor that cancels, while a vertical asymptote stays when a denominator factor does not cancel.
Question 9
Solve (x + 3) / (x - 1) = 2.
Desmos Move: Cross-multiply or multiply both sides by x - 1, then check that your answer does not break the denominator.
Question 10
A rational function has degree 1 in the numerator and degree 2 in the denominator. What is its horizontal asymptote?
Desmos Move: When the denominator degree is greater, the fraction gets closer and closer to 0 as x becomes very large in either direction.