FLVS Algebra 1 Module 2 Study Guide

Relation

A relation is a set of input and output values (ordered pairs).

Function

A function is a special relation where each input has only one output.

Vertical Line Test

If a vertical line touches a graph more than once, it's NOT a function.

Domain

All x-values (inputs).

Range

All y-values (outputs).

Function Notation

f(x) means 'function of x' or 'y-value when x is ___'.

Evaluating Functions

You may be asked to evaluate f(x) for a given x-value, solve for x when given a y-value, or use a graph or table to evaluate function values.

Linear Functions

Linear functions make straight lines (except vertical lines, which are not functions).

Slope

Slope = rise/run = (change in y)/(change in x).

Positive Slope

Line goes up.

Negative Slope

Line goes down.

Slope of 0

Horizontal line.

Undefined Slope

Vertical line.

x-intercept

Where the line crosses the x-axis (y = 0).

y-intercept

Where the line crosses the y-axis (x = 0).

Slope-Intercept Form

y = mx + b (m = slope, b = y-intercept).

Point-Slope Form

y - y1 = m(x - x1) (used when you know a point and a slope).

Standard Form

Ax + By = C (A, B, C are constants).

Parallel Lines

Same slope.

Perpendicular Lines

Slopes are negative reciprocals (e.g., 2 and -1/2).

Comparing Linear Functions

Compare linear functions using graphs, tables, equations, or verbal descriptions.

Increasing Function

y-values go up as x increases.

Decreasing Function

y-values go down as x increases.

Constant Function

y-values stay the same.

Transformations

f(x) + k → shift up, f(x) - k → shift down, f(x + k) → shift left, f(x - k) → shift right, kf(x) → stretch vertically, f(kx) → compress horizontally.