# Maths - Sketching Graphs

> Source: https://ollybritton.com/notes/a-level/maths/topics/sketching-graphs/ · Updated: 2020-10-05 · Tags: maths, school, year-1

##### If the coefficient of $x^3$ is positive, how does a cubic graph look??
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##### If the coefficient of $x^3$ is negative, how does a cubic graph look??
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##### A cubic equation has roots $-1, 2$ and $3$. Visualise it's graph??
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##### What does a graph of $\frac{1}{x}$ look like??
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##### What does a graph of $\frac{1}{x^2}$ look like??
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##### What does a graph of $\frac{-2}{x}$ look like??
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##### What does a graph of $\frac{-5}{x^2}$ look like??
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##### What does a graph of $2^x$ look like??
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##### What does a graph of $\sqrt{x}$ look like??
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##### What does a graph of $\frac{1}{2}^x$ look like??
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### 2022-04-12
##### Rather than sketching $$f(x) = \frac{2}{x - 1} - e^{x}$$ what's a much easier way of showing that $f(x)$ only has one root??
Sketch $e^x$ and $\frac{2}{x - 1}$ separately.

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