Linear Functions

Front

What is a linear function?

Back

A linear function is a function that can be graphically represented as a straight line. It has the form f(x) = mx + b, where m is the slope and b is the y-intercept.

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 graph represents a function?

Back

A graph represents a function if any vertical line drawn through the graph intersects it at most once (Vertical Line Test).

Front

What is the slope of a linear function?

Back

The slope of a linear function is a measure of the steepness of the line, 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 graph of the function crosses the y-axis, representing the output value when the input value (x) is zero.

Front

How do you find the value of a function at a specific point?

Back

To find the value of a function at a specific point, substitute the x-value into the function's equation and solve for f(x).

Front

What is the difference between independent and dependent variables in a function?

Back

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

Front

What is a relation in mathematics?

Back

A relation is a set of ordered pairs, where each pair consists of an input value and its corresponding output value.

Front

What is the significance of the coordinates in a relation?

Back

The coordinates in a relation represent the input-output pairs, where the first number is the x-coordinate (input) and the second number is the y-coordinate (output).