# Exam-Style Question on Graphs

## A mathematics exam-style question with a worked solution that can be revealed gradually

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Question id: 590. This question is similar to one that appeared on an IB AA Standard paper in 2021. The use of a calculator is not allowed.

The function $$f$$ is defined by:

$$f(x) = \frac{4x+2}{x+1}, \quad \text{ where } x \in \mathbb{R}, x \neq -1$$

(a) Write down the equation of the vertical asymptote of the graph of $$f$$.

(b) Write down the equation of the horizontal asymptote of the graph of $$f$$.

(c) Find the coordinates of the $$x$$-axis and $$y$$-axis intercepts.

(d) Sketch the graph of $$f$$.

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