Comparing, Describing, & Constructing Functions

Front

What is a function?

Back

A function is a relation that assigns exactly one output for each input. It can be represented as an equation, a graph, or a table.

Front

What is the slope of a line?

Back

The slope of a line measures its steepness and is calculated as the change in y divided by the change in x (rise/run).

Front

What does the y-intercept represent in a linear function?

Back

The y-intercept is the point where the line crosses the y-axis, representing the value of y when x is 0.

Front

How do you construct a linear function from a word problem?

Back

Identify the initial value and the rate of change, then use the formula y = mx + b, where m is the rate of change and b is the initial value.

Front

What is the equation of a line in slope-intercept form?

Back

The equation of a line in slope-intercept form is written as y = mx + b, where m is the slope and b is the y-intercept.

Front

How do you find the rate of change from a graph?

Back

The rate of change can be found by selecting two points on the graph, calculating the rise (change in y) and run (change in x), and then dividing rise by run.

Front

What is a linear model?

Back

A linear model is a mathematical representation of a relationship between two variables that can be graphed as a straight line.

Front

What does it mean for a function to have a greater rate of change?

Back

A function with a greater rate of change increases or decreases more rapidly than another function over the same interval.

Front

How can you represent a situation where a quantity decreases over time?

Back

You can represent a decreasing quantity with a linear function that has a negative slope.

Front

What is the difference between independent and dependent variables?

Back

The independent variable is the input (often x), while the dependent variable is the output (often y) that depends on the independent variable.