Graphs of Exponents & Logarithms

Maths: Edexcel A Level Pure Maths, topic 6.1.5

Common Functions

To sketch a graph, look at whether it is exponential, reciprocal or some other type of graph. Then plot some $x$ and $y$ coordinates and join them up in the right shape.

Exponential

Exponential

Exponential functions are of the form $y = k^x$ or $y = k^{-x}$ .
They are completely above the $x$ -axis and go through the point $(0, 1)$ .
If $k > 1$ and the power is positive then the graph starts in the bottom left and then has a steep gradient up to the top right.

Reciprocal

Reciprocal

Reciprocal graphs never cross the $x$ or $y$ -axes.
This means the $x$ and $y$ -axes are asymptotes of the reciprocal function.
They are only in 2 quadrants of the graph.
They are usually of the form $y = \frac{a}{x}$ or $xy=a$ .

Test yourself on Graphs of Exponents & Logarithms

What type of graph is this?
What type of graph is this?
What type of graph is y = 3^x?
What type of graph is y = 3^x?
What type of graph is y = 1/x

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