Consider the following piecewise-defined function. f(x){x^2 -5, x< 3
{2x+5, x> 3
find f(-4)

Results from f (-4) = 11

Set A to set B is said to be a function if each member of set A pairs is exactly one member of set B

So, one value of x is only assigned to one value of y, or one input for one output

A function can be expressed in the form of a diagram, the set of ordered pairs, or arrow diagrams

If y is a function of x, then y = f (x)

where x is the independent variable and y is the dependent variable

x is the domain and y is the result area or range

There are several forms of function including:

• 1. linear function

• 2. quadratic function

• 3. trigonometric functions

• 4. polynomial function

• 5. fraction function etc.

A function can be write as ordered pair

Ordered pairs because we write the input first, and then the output

Can be described in form

(input, output)

or

(x, f (x))

For example a set of ordered pairs

(2,4), (3,5), (4,6)

input values (as domain) 2,3,4

output values (as range) 4,5,6.

Piecewise Functions: functions that have different equations based on the input (x) value

A function made up of 2 pieces:

if we look for f (-4), then:

Because -4 is <3, so we use f (x) = x²-5, so

F (x) = x2 + 1 g (x) = 5 - x

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the inverse of the function f (x) = 2x-10

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domain of the function

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