Evaluate a linear function

Learning Objectives Define what a linear function is and identify its components. Understand and correctly use function notation, such as f(x). Substitute a given numerical value for the input variable in a linear function's equation. Apply the order of operations (PEMDAS) to accurately calculate the output of a linear function. Interpret the meaning of an evaluated linear function in real-world contexts. Distinguish between the input and output of a linear function. Ever wonder how a store calculates your total bill based on the number of items you buy? 🛒 Or how scientists predict temperature changes? 🌡️ In this lesson, you'll learn how to 'evaluate' linear functions, which means finding the output of a function when you know its input. This skill is f...

TermDefinitionExample FunctionA special relationship where every input has exactly one output.The relationship between the number of hours worked and the money earned (for a fixed hourly wage) is a function. Linear FunctionA function whose graph is a straight line and can be written in the form y = mx + b or f(x) = mx + b.y = 2x + 3 is a linear function. Its graph is a straight line. Input (Domain)The value you put *into* the function, usually represented by 'x'. It's the independent variable.In the function f(x) = 2x + 3, if you choose x = 5, then 5 is the input. Output (Range)The value that comes *out* of the function after applying the rule, usually represented by 'y' or 'f(x)'. It's the dependent variable.In the function f(x) = 2x + 3, if the in...

Standard Form of a Linear Function $$y = mx + b$$ This is a common way to write a linear function, where 'm' is the slope (rate of change) and 'b' is the y-intercept (starting value). To evaluate, substitute the given 'x' value into the equation and simplify. Function Notation for a Linear Function $$f(x) = mx + b$$ This notation is equivalent to y = mx + b. f(x) represents the output value for a given input x. To evaluate f(a), substitute 'a' for every 'x' in the function's rule. Process of Evaluation To evaluate $f(a)$, replace every instance of $x$ in the function's rule with the specific value $a$, then simplify the expression using the order of operations (PEMDAS/BODMAS). This rule guides the step-by-st...