LESSON 3

ELEMENTARY FUNCTIONS

"f(x) = ... " is the classic way of writing a function. And there are other ways, as you will see!

TEST - WHAT HAVE I LEARNED

Q3

Q1

Q2

Q6

Q4

Q5

Q10

Q7

Q8

Q9

Types of functions

A linear function is of the form f(x) = mx + b where 'm' and 'b' are real numbers.

A quadratic function is a polynomial function with one or more variables in which the highest exponent of the variable is two.

The definition of inverse proportion states that "Two quantities are said to be in inverse proportion if an increase in one leads to a decrease in the other quantity and a decrease in one leads to an increase in the other quantity".

A radical function is any function that is defined in a root. This function also contains a square root, cubed roots, or any of the nth root.

An absolute value function is an important function in algebra that consists of the variable in the absolute value bars.

A piecewise function is a function with multiple pieces of curves in its graph. It means it has different definitions depending upon the value of the input. i.e., a piecewise function behaves differently for different inputs.

EXERCISES

Associate the graphs with the equations above

inverse proportion

linear

quadratic

radical

Associate the graphs with the equations above

Obtain the analytical expressions of the following piecewise functions

Function transformation

Domain

check your knowledge

Find the domain of the following functions:

and some other combinations that will be written on the blackboard . . .

with square roots, logarithms, like this one

EXTRA WORK

webgraphy

Google images https://www.mathsisfun.com/sets/function.html https://www.mathsisfun.com/sets/set-builder-notation.html https://www.highermathematics.co.uk/domain-restrictions/ https://www.math-exercises.com/analysis-of-functions/domain-of-a-function https://www.cuemath.com/calculus/linear-functions/ https://www.cuemath.com/calculus/quadratic-functions/ https://www.cuemath.com/commercial-math/inverse-proportion/ https://www.cuemath.com/algebra/absolute-value-function/ https://www.cuemath.com/calculus/piecewise-function/ https://www.cuemath.com/calculus/transformation-of-functions/