1. Pure Algebra

Rational Functions — Quiz

Test your understanding of rational functions with 5 practice questions.

Practice Questions

Question 1

When integrating a rational function, if the denominator contains a non-repeated irreducible quadratic factor like $(ax^2+bx+c)$ (where $b^2-4ac < 0$), what is the correct form of the partial fraction corresponding to this factor?

Question 2

What is the result of differentiating the rational function $f(x) = \frac{2x}{x^2+4}$?

Question 3

When sketching the graph of a rational function, what is the significance of the roots of the numerator?

Question 4

Consider the rational function $f(x) = \frac{x^2 - 16}{x - 4}$. What is the behavior of the graph at $x = 4$?

Question 5

When integrating a rational function, if the denominator contains a repeated irreducible quadratic factor like $(ax^2+bx+c)^2$, what is the correct form of the partial fractions corresponding to this factor?