Functions, Linear Equations, and Transformations

Vocabulary flashcards covering key concepts of functions, linear equations, notation, graphing methods, transformations, and absolute value functions.

Function

A relationship where every input has exactly one output.

Domain

All possible $x$-values (inputs).

Range

All possible $y$-values (outputs).

Relation

A set of ordered pairs $(x, y)$.

Independent variable

The input ($x$-value).

Dependent variable

The output ($y$-value).

Vertical Line Test

A rule stating that if a vertical line crosses a graph more than once, it is NOT a function.

Increasing function

A function that goes up from left to right.

Decreasing function

A function that goes down from left to right.

Constant function

A function that stays flat; does not change.

Linear function

A straight-line graph.

Nonlinear function

A graph that is not a straight line.

Piecewise function

A function with different rules for different parts.

Even function

A function that is symmetrical over the $y$-axis.

Odd function

A function that is symmetrical around the origin.

Slope ($m$)

How steep a line is.

$Y$-intercept ($b$)

Where the line crosses the $y$-axis.

$X$-intercept

Where the line crosses the $x$-axis.

Standard form

$$Ax + By = C$$

Slope-intercept form

$$y = mx + b$$

Parallel lines

Lines that never cross; same slope.

Perpendicular lines

Lines that cross at a $90^\circ$ angle; opposite reciprocal slopes.

Function notation

Writing a function as $f(x)$.

Evaluate a function

Put a number in for $x$ and solve.

Input/output

Input is $x$; output is $y$.

Composite function

Putting one function inside another: $f(g(x))$.

Inverse function

A function that reverses the original function.

Intercepts method

Find the $x$- and $y$-intercepts and connect them.

Slope method

Find a point and use the slope to graph the line.

Horizontal line

A flat line with slope $0$; equation $y = b$.

Vertical line

An up-and-down line with undefined slope; equation $x = a$.

Rise over run

Move up or down, then left or right.

Point-slope form

$$y - y_1 = m(x - x_1)$$

Slope triangle

A triangle used to show rise and run.

Vertical shift

Moves the graph up or down.

Horizontal shift

Moves the graph left or right.

Reflection over $x$-axis

Flips the graph upside down.

Reflection over $y$-axis

Flips the graph left to right.

Vertical stretch

Makes the graph steeper.

Vertical compression

Makes the graph less steep.

Slope change

Changes how steep the line is.

Absolute value function

A V-shaped graph: $y = |x|$.

Vertex

The turning point of the graph.

Axis of symmetry

The line that splits the graph into two equal halves.

Piecewise definition

Shows the different rules for each part of a function.

Transformations

Changes the graph's position, direction, or shape.