Images, preimagesAs we have seen in the 8th Grade lesson, a function is a machine to which you give numbers and gives you other numbers in return. Let's take the function , and see what happens when you give it the numbers 0, 1, 4, 9.It enables us to plot the graph of the function : 1 is called the image of 4 under f. 9 is called a preimage of 2 under f. Don't forget that the x values have to be found on the Xaxis (horizontal) and that the f(x) values are to be found on the Yaxis. If you want to solve the equation thanks to a graph, you have to find all the x's on the Xaxis such that . You can draw a horizontal line of height 1, and find the values of x where the line and the graph intersect. Solving such an equation is equivalent to finding the preimages of 1 under f. DomainsBe careful : you can't always calculate the number the function will give. For example,You can't calculate f(2) because it's impossible to divide by zero : The closer to zero the number under the bar, the greater the result. Actually, when you divide by zero, the result it infinite and infinity is not a number, that's why we say that it's impossible to divide by zero. The set of values of x for which it is possible to calculate f(x) is called the domain of the function. Consider the function ,its domain is . Which means all the numbers except 2. If , then , which means all the positive numbers (You can't calculate the square root of a negative number). Monotony of a functionA function is said to be increasing if its graph goes up. In that case, with two numbers a<b on the Xaxis, we get f(a)<f(b) :A function is said to be decreasing if its graph goes down. In that case, with two numbers a<b on the Xaxis, we get f(a)>f(b) : ParityWell, one day it will be successful...More seriously :
Square function
Inverse function
