Practice Set 6
10 Rational Readiness Questions
This final mixed set checks restrictions, graph features, simplification, and rational-equation accuracy in one quick readiness check.
Practice Questions
Mixed Readiness Check: Rational Functions
Finish with a balanced rational review that checks whether you can move between direct skills, graph interpretation, and equation solving with steady confidence.
Question 1
Which statement is true for y = (x - 1) / (x + 4)?
Desmos Move: Use the numerator for the x-intercept and the denominator for the vertical asymptote.
Question 2
Solve 4 / x = 1 / 3.
Desmos Move: Cross-multiply or think about what x must be so that 4 divided by x equals one-third.
Question 3
The graph shown has a hole at x = 1 and follows the line y = x + 2 everywhere else. Which expression could produce that graph?
The graph follows a line but has one missing point from a canceled factor.
Desmos Move: Factor the numerator and see which expression simplifies to x + 2 while still excluding x = 1.
Question 4
Why is x = -3 not a valid solution to (x + 3) / (x + 3) = 1?
Desmos Move: The expression simplifies to 1 only for allowed x-values. The original denominator still matters.
Question 5
For f(x) = 2 / (x - 5), what is f(7)?
Desmos Move: Substitute directly, then simplify the fraction. This is a good quick calculator check if needed.
Question 6
A snack stand models average profit per item as 96 / x, where x is the number of items sold. Which restriction makes sense?
Desmos Move: Ask what x means in the situation. A number of items sold should fit the real-world context.
Question 7
Which rational function has horizontal asymptote y = 0?
Desmos Move: Compare the degrees. A larger denominator degree usually means the graph approaches y = 0.
Question 8
Solve (x - 2) / (x + 3) = 4.
Desmos Move: Multiply both sides by x + 3, solve the linear equation, and then check that the answer is not x = -3.
Question 9
A student says the graph of y = 5 / (x - 2) has y-intercept 5. What is the best correction?
Desmos Move: The y-intercept always happens when x = 0. Use that rule even for rational functions.
Question 10
Which action is most important after solving a rational equation?
Desmos Move: A quick substitution into the original equation or a check in Desmos can save you from keeping an extraneous solution.