Understanding Functions

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 domain of a function?

Back

The domain of a function is the set of all possible input values (x-values) for which the function is defined.

Front

What is the range of a function?

Back

The range of a function is the set of all possible output values (y-values) that the function can produce.

Front

How do you determine if a relation is a function?

Back

A relation is a function if every input has exactly one output. This can be checked using the vertical line test.

Front

What is a linear function?

Back

A linear function is a function that can be graphically represented as a straight line, typically in the form y = mx + b.

Front

What does the slope of a line represent?

Back

The slope of a line represents the rate of change of the function, indicating how much y changes for a unit change in x.

Front

What is the y-intercept?

Back

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

Front

Write the equation for a linear function with a slope of 2 and a y-intercept of 3.

Back

y = 2x + 3.

Front

What is the difference between independent and dependent variables?

Back

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

Front

What is a table of values in relation to functions?

Back

A table of values lists pairs of input (x) and output (y) values to show how a function behaves.