Multiple Representations

Front

What is a function?

Back

A function is a relationship between two sets of values where each input (x) is related to exactly one output (y).

Front

What does it mean for a variable to be dependent?

Back

A dependent variable is one whose value depends on the value of another variable. For example, in the equation W(t) = 10t, W is dependent on t.

Front

What does it mean for a variable to be independent?

Back

An independent variable is one that can be changed or controlled in an experiment. It is not affected by other variables. For example, in the equation W(t) = 10t, t is independent.

Front

How do you represent a linear relationship?

Back

A linear relationship can be represented by an equation of the form y = mx + b, where m is the slope and b is the y-intercept.

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/run).

Front

What is the y-intercept?

Back

The y-intercept is the point where a line crosses the y-axis, represented by the value of y when x = 0.

Front

How can you represent a real-world situation with a function?

Back

You can represent a real-world situation with a function by identifying the dependent and independent variables and creating an equation that relates them.

Front

What is a table of values?

Back

A table of values is a way to organize pairs of input (x) and output (y) values to show the relationship defined by a function.

Front

What is a graph in mathematics?

Back

A graph is a visual representation of data or a function, showing the relationship between variables on a coordinate plane.

Front

How do you determine if a relationship is linear from a graph?

Back

A relationship is linear if the graph forms a straight line.