Practice Set 3
10 Strategic Questions
This set focuses on explaining restrictions, justifying graph behavior, and applying rational functions in EOC-style contexts.
Practice Questions
DOK 3 Practice Set: Rational Reasoning
Use Desmos to test claims, compare graph behavior, and support your reasoning when restrictions and asymptotes make the algebra more subtle.
Question 1
A student says (x² - 1) / (x - 1) = x + 1 for all real x. Which response is best?
Desmos Move: Graph both expressions in Desmos and zoom near x = 1. You will see the simplified line and the missing point from the original expression.
Question 2
Solve (x + 2) / x = 3 and give the valid solution.
Desmos Move: Multiply both sides by x, solve the linear equation, and then check that your answer does not violate the restriction x ≠ 0.
Question 3
Which equation could match the graph with a hole at x = -2 and a vertical asymptote at x = 1?
Desmos Move: Use the canceled factor for the hole and the remaining denominator factor for the vertical asymptote.
Question 4
A school club shares a $240 bus cost among x students. Which expression models the cost per student if each student also pays a $5 ticket fee?
Desmos Move: The shared part changes with the number of students, but the ticket fee stays fixed for each student.
Question 5
In the bus-cost model 240 / x + 5, what does the domain restriction x ≠ 0 mean in context?
Desmos Move: Translate the algebra restriction back into the real situation. Ask what x represents before interpreting the restriction.
Question 6
Function A has a vertical asymptote at x = 3 and Function B has a hole at x = 3. Which statement is true?
Desmos Move: Think about what happens exactly at x = 3 and also what happens when x gets close to 3 from each side.
Question 7
For f(x) = a / (x - 2), if the graph passes through (4, 3), what is the value of a?
Desmos Move: Substitute the point into the equation. Using a known point is often the fastest way to find the missing constant.
Question 8
The function (x² - 4) / (x - 2) has a hole at x = 2. What is the y-value of the hole?
Desmos Move: Simplify first, then substitute the excluded x-value into the simplified expression to find the missing point.
Question 9
A student solves (x - 3) / (x - 3) = 1 and says every real number is a solution. Which correction is best?
Desmos Move: The simplified expression may look constant, but the original denominator still controls the restriction.
Question 10
Near the vertical asymptote x = 1, the graph shown goes to negative infinity on the left and positive infinity on the right. Which function best matches that behavior?
Compare left-side and right-side behavior near the vertical asymptote.
Desmos Move: Graph y = 1 / (x - 1) and y = -1 / (x - 1) together in Desmos. The sign changes which side rises and which side falls.