MD Memahami Fungsi Matematika

A basic mathematical function is a rule that pairs each value of the independent variable (input) with exactly one value of the dependent variable (output). It is generally denoted as (f(x) = y). The main application is to substitute the value (x) into an equation to obtain the value (y). Let's examine the three most basic functions in mathematics and their applications: 1. Linear Functions. This function has the general formula (f(x) = ax + b) (where (a) is the gradient and (b) is a constant). Its graph is a straight line. Example Application: If the function formula for a taxi fare is (f(x) = 7000x + 15000) (where (x) is the distance traveled in kilometers). To find the total cost of traveling a distance of (5) km, simply plug the value (x) into the formula: (f(5) = 7000(5) + 15000) (f(5) = 35000 + 15000 = 50000). So, the total cost is Rp50,000.2. Quadratic Function: This function has the general formula (f(x) = ax^2 + bx + c). Its graph forms a parabolic curve. Application Examples: The most common applications are in physics. For example, the formula for the height of a ball (in meters) versus time (in seconds) is (h(t) = -5t^2 + 20t). To find the height of the ball at the second second, apply the following substitution: (h(2) = -5(2)^2 + 20(2)) (h(2) = -5(4) + 40) (h(2) = -20 + 40 = 20). So, at the second second, the ball reaches a height of (20) meters. How to Determine a Function Formula If you don't know the function formula, you can find it using the two existing coordinates (elimination and substitution). Example of Application: Determine the formula of the linear function (f(x) = ax + b) if the values ​​​​(f(1) = 5) and (f(-1) = 1) are known. The form of the equation is: (a(1) + b = 5 rightarrow a + b = 5) (a(-1) + b = 1 rightarrow -a + b = 1) By eliminating the value of (b), the values ​​​​(a = 2) and (b = 3) are obtained, so the exact function formula is (f(x) = 2x + 3).