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# Functions and Graphs (Metric)

## Class Details

Tom Baker

This class covers the idea of a function, composites and inverses, odd and even functions and specific functions including the modulus function, the exponential and logarithmic functions and the hyperbolic functions. Some of this is covered at A-level, and most of the rest is Further Maths.

## Units

### Functions in General

Composites, inverses, odd and even functions. This is an A-level topic, which Science and Engineering courses at Imperial will assume you know.

Functions of the form $$f(g(x))$$ for given $$f$$ and $$g$$.

The inverse of a given function.

Lesson

Odd and even functions; the odd and even parts of a function.

Lesson

### Particular Functions

Modulus, Heaviside step, exponential and logarithmic functions. Apart from the Heaviside function, which is a university topic, this is covered at A-level and Science and Engineering courses will assume you know it.

The function $$y=|x|$$; composition with other functions; solving equations and inequalities.

Lesson

The Heaviside step function $$H(x)$$, and its use in characterising piecewise functions.

Lesson

Exponential functions in general, and the exponential function, $$y=e^x$$; laws of exponents, and simplifying expressions involving exponentials.

Lesson

Logarithmic functions in general, and the natural logarithm; laws of logarithms and the change of base theorem. Simplifying expressions.

Lesson

### Hyperbolic Functions

The functions $$\sinh x$$, $$\cosh x$$ and $$\tanh x$$, and their reciprocals and inverses. This is a Further Maths topic; Imperial courses that require Further Maths may assume you know it.

The functions $$\sinh x$$, $$\cosh x$$ and $$\tanh x$$ and their reciprocals. Solving equations involving them.

Lesson

The inverse functions $$\sinh^{-1}\,x$$, $$\cosh^{-1}\,x$$ and $$\tanh^{-1}\,x$$; logarithmic form for each.

Lesson

The relationship between hyperbolic identities and trigonometric identities.

Lesson
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