In Section A, Unit 9, we learned that a function is like a machine that has an input and an output. The output is related somehow to the input.
Input Function Output
By the end of this section you should: ● understand what a linear function is ● be able to graph a linear function
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Important terms and symbols Input
x x
domain
independent variable n
Output y
f (x)
range ∈ codomain dependent variable Tn (term value)
Till computer
A function is an equation for which any input will give exactly one output.
Commonly used in
Coordinate geometry and linear equations Functions Functions Functions Patterns
An independent variable is a variable (often denoted by x ) whose value does not depend on that of another.
A dependent variable (often denoted by y ) is a variable whose value depends upon independent variable x.
Linear functions A linear function has the following form.
y = f (x) = a + bx
A linear function has one independent variable (x) and one dependent variable (y). a is the constant term or the y -intercept.
a run
Linear functions are those whose graph is a straight line.
y f (x) rise
b = rise run
x
b is the coeffi cient of the independent variable. It is also known as the slope and gives the rate of change of the dependent variable. ●
●
f (a) means if the input ( x) is a , what is the output ( y )? (Where a is number or variable) f (x) = a means if the output (y) is a , what is the input ( x)? (Where a is some number or variable)
f (x) is pronounced ‘ f of x ’ It can also be written in the following three ways: f →x