Computations can become confusing when you must use several formulas and/or equations for the same problem.
Function notation was developed to help differentiate between distinct equations and formulas, which are all considered functions.
Function notation refers to switching out the output’s variable (usually y) with a different notation: f(x). This notation is not f multiplied to x, but is simply read as “f of x.”
The f is a label or a way to distinguish which equation is which. You can use whatever letter you want for function notation, but many functions will be paired with the f. The variable inside of the parenthesis is the input.
A function is a correspondence, or relation, between two sets of data where each input (one set of data) is associated with one output (second set of data). In other words, inputting a specific value into an equation or formula will result in one specific output value.
Area of a circle
A = πr2 can written in function notation as f(r) = πr2
Area of a square
A = s2 can written in function notation as f(s) = s2
y = mx + b can written in function notation as f(x) = mx + b
y = ax2 + bx + c can written in function notation as f(x) = ax2 + bx + c
If an input results in more than one output, the equation or formula cannot be considered a function.
We can use the vertical line test to understand visually if an equation is also a function. For example, take y = x2, which is shown below:
If you draw a vertical line through the graph, it only touches the graph in one place. That means for a value of x, there is only one value of y.
Therefore, it is a function.
But now let's look at the equation x = y2. Its graph is shown below.
If you draw a vertical line through the graph, it touches the graph in multiple places. That means that for a value of x, there are multiple values of y.
Therefore, it is not a function.
If f(x) = 3x + 4, find f(3).
If g(x) = x2 + 5x + 7, find g(5).
If h(p) = p3 - 2p, find h(2)
If q(r) = 5r2 + 2r + 3, find q(3)
If f(x) = 2x + 7, find f(a+3)