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In this lesson, you will learn the basics of functions. You will understand their notation, and how they work. You will look at some starter exercises. Refer to the video tutorial for additional help, as well as our Reddit if necessary: r/MezeiMaths
Video Tutorial
✔ Approved by qualified IB Teacher
What are Linear Functions?
A linear function is a function who's graph is a straight line. This esensially means that the value of the function changes with a constant value. It is denoted like:
f(x)=ax+b
Read as "f of x, is equal to a times x plus b"Where a is the coefficient for x, and b is the contant term, meaning that it doesn't change regardless of x.The f(x) here is a basic reqirement for understanding functions. f(x) is the dependent variable, so that when x changes, the value of f(x) does so too. It, f(x), can be thought of as a machine that takes in a value, x, and turns it into another value, which would be the value of f(x). As an example, if f(x) = 2x, then the machine will multiply the input value by 2. So if the input value, x, is 5, the machine will multiply that by two, and turn it into 10, which will be the value of f(2). So:
f(x) = 2*x
f(2) = 2*5
f(2) = 10
The value of f(x) if x = 2, is therefore 10.
What are quadratic functions?
Quadratic functions are functions that include the variable of the function to taken to the power of 2. For instance :
f(x)=ax^2+b
A quadratic function on a graph will have the shape of a parabola. Depending on the operator in front of constant a. So if the operator in front of a is
-
the parabola will be upside down, forming a sad face. (Fig. 1) On the other hand, if the operator is
+
it will be upside up, forming a happy face. (Fig. 2)
(Fig. 1) Quadratic function with negative operator in front.
(Fig. 2) Quadratic function with positive operator in front.
Worked Example 1: Let f(x) = 5x + 5 with x = 2. Solve for f(2)
Worked Example 1: Let f(x) = 5x + 5 with x = 2. Solve for f(2)
Let f(x) = 5x + 5 with x = 2. Solve for f(2).
Substitute each x by 2:
f(2) = 5(2) + 5 = 10 + 5 = 15
Answer:
15
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