Waste less time on Facebook — follow Brilliant.
Already have an account? Log in here.
Rational Functions
A rational function can have a variable like "x" in the numerator AND the denominator. When this happens, there are some special rules and properties to consider.
True or false:
All rational functions have some form of asymptote, whether it's slant, vertical, or horizontal.
Already have an account? Log in here.
by
Hobart Pao
How many vertical asymptotes are there on the following rational function?
\[f(x) = \frac{x^{356} - 123x^{22} - 43x^{2}+10123}{x}\]
Already have an account? Log in here.
by
Spencer Whitehead
\[ f(x) = \dfrac{(x-1)(x-2)(x-3)(x-4)(x-3)(x-2)(x-1)}{(x-2)(x-4)(x-2)}\]
How many values of \( x \) satisfy the equation \( f(x) = 1 \) ?
Already have an account? Log in here.
by
Pranshu Gaba
\[f(x)=\dfrac{x^2-6x+6}{2x-4}\] \[g(x)=\dfrac{ax^2+bx+c}{x-d}\]
You are given two functions \(f\) and \(g\) above, where \(a, b, c,\) and \(d\) are unknown constants. Also, you are given the following information about the function \(g\):
It has the same vertical asymptote as \(f\).
Its diagonal asymptote is perpendicular to that of \(f\), and these two asymptotes intersect each other on the \(y\)-axis.
The graphs of \(f\) and \(g\) have two intersection points. One of them is at \(x = -2\). (In other words, \(f(-2) = g(-2)\).)
What is the value of the other \(x\)-coordinate where \(f\) and \(g\) intersect?
Already have an account? Log in here.
by
Arjen Vreugdenhil
Let \(x\) be a real number. Consider the function
\[ f(x) = \frac{x^3 - 1}{x^2 + x - 2} \]
How many real zeroes does it have?
Already have an account? Log in here.
by
Denton Young