Evaluate a linear function

Learning Objectives Define a linear function and understand function notation. Substitute a given input value into a linear function's equation. Accurately perform arithmetic operations to find the output value of a linear function. Distinguish between input and output values in a function. Interpret the meaning of an evaluated linear function in a real-world context. Ever wonder how a vending machine knows what drink to give you when you press a button? 🥤 It's like a mathematical function where your button press is the input, and the drink is the output! In this lesson, you'll learn how to 'evaluate' linear functions, which means finding the output value when you know the input. This skill is crucial for understanding how different quantities relate...

TermDefinitionExample FunctionA rule that assigns exactly one output value for each input value.For every student in a class (input), there is exactly one student ID number (output). Linear FunctionA function whose graph is a straight line. It can be written in the form $y = mx + b$ or $f(x) = mx + b$.$f(x) = 2x + 3$ is a linear function. Input (Domain)The value you put *into* the function, usually represented by 'x'.In $f(x) = 2x + 3$, if you choose $x=1$, then 1 is the input value. Output (Range)The value that comes *out* of the function after applying the rule, usually represented by 'y' or $f(x)$.In $f(x) = 2x + 3$, if $x=1$, then $f(1) = 2(1)+3 = 5$. So, 5 is the output value. Function NotationA way to write functions using symbols like $f(x)$, read as 'f of...

Linear Function Standard Form $f(x) = mx + b$ This is the general form of a linear function, where 'm' represents the slope (rate of change) and 'b' represents the y-intercept (the starting value or value when x=0). Rule for Evaluating a Function To evaluate $f(x)$ at a specific input value, say $x=a$, substitute 'a' for every 'x' in the function's expression: $f(a) = m(a) + b$. This rule tells you exactly how to find the output value when you are given an input value. Replace the variable 'x' with the given number and then perform the necessary calculations.