Rational and reciprocal functionsIB MYP Maths Extended: Flashcards

What these 13 flashcards ask

What shape is the graph of y=\frac kx?
Where are the branches of y=\frac kx when k0?
Where are the branches of y=\frac kx when k<0?
Asymptotes of y=\frac kx?
Why does y=\frac kx have no intercepts?
Asymptotes of y=\frac{k}{x-a}+b?
How do you find the y-intercept?
How do you find the x-intercept?
Asymptotes of y=\frac{2}{x+3}-1?
Rewrite \frac{x+1}{x-2}.
What is true of x and y on y=\frac kx?
What does a horizontal asymptote mean in a cost model?
Why must a model's domain be checked?

Exam questions on Rational and reciprocal functions

Consider the function $f(x)=\dfrac{6}{x}$ , for $x\neq0$ .
Explain why the graph of $y=f(x)$ crosses neither axis.2 marks
Consider the function $g(x)=\dfrac{2}{x-3}+1$ , for $x\neq3$ .
Find the exact coordinates of the point where the graph of $y=g(x)$ crosses the $x$ -axis.2 marks
Consider the function $h(x)=\dfrac{x+1}{x-2}$ , for $x\neq2$ .
Show that $h(x)=1+\dfrac{3}{x-2}$ , and hence write down the equations of the asymptotes of the graph of $y=h(x)$ .3 marks

Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).