A function f (x) takes values of a variable x from a set called the domain and sends them to values y in a set called the codomain so that each value of x is sent to one and only one value of y.
f (x) Input x 2. Domain and range:
Domain: The domain of a function is the set of values which is mapped by a function.
Range: The range of a function is the set of images obtained by mapping the elements of the domain.
3. Test for a function (vertical line test): y = f (x) is a function if all lines drawn parallel to the y-axis through all points in the domain of f (x) intersect the graph of y = f (x) once and only once.
y P( c– m ––, 0) x
(c) Forms of the equation of a straight line: (y − y1) = m(x − x1)
or y = mx + c or
ax + by + c = 0 y = f (x) x
6. Quadratic functions: (a) Equation: y = ax 2 + bx + c (b) Shapes:
a > 0 a < 0 Operation Output y
4. Combining functions: f ( g (x)) = ( f o g)(x) u = g (x) ⇒ f ( g (x)) = f (u)
5. Linear functions: (a) Equation: y = mx + c (b) Shape:
