Practice Set 1
10 Foundational Questions
This set focuses on domain restrictions, asymptotes, holes, intercepts, and simplifying rational expressions.
Practice Questions
DOK 1 Practice Set: Rational Foundations
Use Desmos to support quick checks while you identify restrictions, asymptotes, holes, intercepts, and basic simplifications.
Question 1
What is the domain restriction for f(x) = (x + 1) / (x - 4)?
Desmos Move: In Desmos, graph the function and notice the break in the graph at x = 4. The denominator tells you exactly which value is excluded.
Question 2
What is the vertical asymptote of g(x) = 3 / (x + 2)?
Desmos Move: Type the function in Desmos and look for the vertical line the graph approaches on both sides.
Question 3
What is the horizontal asymptote of h(x) = (2x + 5) / (x - 1)?
Desmos Move: For rational functions with the same degree on top and bottom, compare the leading coefficients to predict the horizontal asymptote.
Question 4
For r(x) = (x² - 9) / (x - 3), what x-value creates the hole?
Desmos Move: Factor the numerator, cancel the common factor, and remember the canceled value still leaves a missing point.
Question 5
What is the x-intercept of y = (x - 2) / (x + 5)?
Desmos Move: An x-intercept happens when y = 0, so look for where the numerator equals 0 while the denominator stays nonzero.
Question 6
What is the y-intercept of y = (x + 1) / (x - 2)?
Desmos Move: To find the y-intercept, substitute x = 0 and read the output. Desmos can confirm the point on the y-axis.
Question 7
Which expression is equivalent to (x² - 16) / (x - 4) for x ≠ 4?
Desmos Move: Factor the numerator first. The simplified rule is easier to see after canceling the common factor.
Question 8
What is the domain of y = 1 / [(x - 1)(x + 3)]?
Desmos Move: Find every x-value that makes the denominator 0. Each one becomes a restriction in the domain.
Question 9
As x becomes very large, what value does f(x) = 3 / (x - 1) approach?
Desmos Move: Trace the graph far to the right in Desmos. The branch gets closer and closer to the x-axis.
Question 10
Solve (x + 1) / (x - 2) = 0.
Desmos Move: A rational expression equals 0 when its numerator is 0 and its denominator is not 0.