IB Mathematics Analysis and Approaches Topic SL…

Let $g(x)=\frac{p x+1}{q x-r}$ , where $x \neq \frac{r}{q}$ and $p, q, r \in \mathbb{Z}$ . The graph of $y=g(x)$ has a vertical asymptote at $x=-1$ and a horizontal asymptote at $y=2$ . It intersects the $y$ -axis at the point $\mathrm{C}\left(0,-\frac{1}{3}\right)$ .

Write down the domain and range of the graph of $y=g(x)$ .

Determine the values of $p, q$ , and .

Let $f(x)=\frac{4 x+2}{2 x-1}$ , for .

Consider the function $f(x)=\frac{5 x+2}{x-3}$ , where .

A function $f$ is defined by $f(x)=\frac{3 x+2}{x-2}$ , where . The graph of has a vertical asymptote and a horizontal asymptote.

Consider the function $f(x) = \frac{4}{x-3} - 2$ , for .

Find the $x$ -intercept of the graph of $y=g(x)$ .

Sketch the graph of $y=g(x)$ , indicating the asymptotes and the intercepts.

Find the $y$ -intercept of $f$ .

Write down $\lim _{x \rightarrow \infty}\left(\frac{4 x+2}{2 x-1}\right)$ .

Find the $x$ -intercept of the graph of $f$ .

Determine the vertical asymptote of $f$ .

Sketch the graph of $f$ , clearly indicating the $x$ -intercept and the vertical asymptote.

Write down the vertical asymptote.

Write down the horizontal asymptote.

Sketch the graph of $y=f(x)$ on the axes below. On your sketch, clearly indicate the asymptotes and the coordinates of any points of intersection with the axes.

Hence, solve the inequality $0<\frac{3 x+2}{x-2}<3$ .

Solve the inequality $0<\frac{3|x|+2}{|x|-2}<3$ .

The function $f$ is undefined at $x=k$ . State the value of $k$ .

Write down the equation of the horizontal asymptote of the graph of $f$ .

Find the coordinates of the $x$ -intercept of the graph of $f$ .

The graph of $f$ intersects the $y$ -axis at the point $(0, p)$ . Find the value of $p$ .

IB Mathematics Analysis and Approaches SL 2.8—reciprocal and Simple Rational Functions, Equations of Asymptotes Questionbank

IB Mathematics Analysis and Approaches (AA) Topic SL 2.8—reciprocal and Simple Rational Functions, Equations of Asymptotes Questionbank