Functions and Graphs Flashcard

Front

What is a function?

Back

A function is a relation between a set of inputs and a set of possible outputs where each input is related to exactly one output.

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, calculated as the change in y divided by the change in x (rise over run).

Front

How do you calculate the rate of change of a function?

Back

The rate of change is calculated by taking the difference in the y-values divided by the difference in the x-values between two points on the graph.

Front

What does it mean if a graph is increasing?

Back

A graph is increasing if, as you move from left to right, the y-values are getting larger.

Front

What does it mean if a graph is decreasing?

Back

A graph is decreasing if, as you move from left to right, the y-values are getting smaller.

Front

What is a y-intercept?

Back

The y-intercept is the point where a line crosses the y-axis, represented as (0, y).

Front

How do you find the y-intercept from a slope and a point?

Back

Use the formula y = mx + b, where m is the slope and (x, y) is the point. Rearrange to solve for b.

Front

What is a linear function?

Back

A linear function is a function that graphs to a straight line, defined by the equation y = mx + b.

Front

What is the formula for slope between two points (x1, y1) and (x2, y2)?

Back

The formula for slope (m) is m = (y2 - y1) / (x2 - x1).

Front

What does a slope of 0 indicate about a line?

Back

A slope of 0 indicates that the line is horizontal and there is no change in y as x changes.