Evaluating Functions – Key Vocabulary

Vocabulary flashcards summarizing essential terms and real-world function models from the lecture on evaluating functions.

Evaluating Functions

The process of finding the output (y) of a function for a given input (x) by substituting x into the function rule.

Dependent Variable

The variable (often y or f(x)) whose value depends on the chosen input value; the output of a function.

Independent Variable

The variable (often x) that is freely chosen or given, determining the value of the dependent variable in a function.

Function Notation (f(x))

A symbolic way to represent a function, showing the output (f(x)) produced by an input x.

Substitution

Replacing the variable x in a function with a specific numerical value to evaluate the function.

Simplify

The algebraic step of carrying out arithmetic operations (e.g., multiplication, addition) after substitution to reduce an expression to its simplest form.

Combine Like Terms

Adding or subtracting terms with the same variables and exponents to condense an expression, especially useful after simplifying.

Linear Function

A function of the form f(x)=mx+b where the graph is a straight line; example: f(x)=5x+3.

Quadratic Function

A polynomial function of degree two, typically written as f(x)=ax²+bx+c, which graphs as a parabola.

Rate (in functions)

A ratio that relates two quantities and serves as the constant of proportionality in many linear models (e.g., 60 km per hour).

Distance Function D(t)=60t

A linear model where distance D depends on time t, with the car traveling 60 kilometers every hour.

Cost Function C(x)=40x

A linear model where total cost C depends on the number of meals x, with each meal costing Php 40.

Laundry Time Function f(x)=2x

A function representing Rose’s washing time: it takes 2 hours per basket, so x baskets require 2x hours.