Linear Functions

Front

What is a linear function?

Back

A linear function is a function that graphs to a straight line. It can be expressed in the form f(x) = mx + b, where m is the slope and b is the y-intercept.

Front

What does the slope (m) represent in a linear function?

Back

The slope (m) represents the rate of change of the function. It indicates how much the output (y) changes for a unit change in the input (x).

Front

What is the y-intercept in a linear function?

Back

The y-intercept is the point where the graph of the function crosses the y-axis. It is represented by the value of b in the equation f(x) = mx + b.

Front

How do you find the output value of a linear function for a given input?

Back

To find the output value, substitute the input value (x) into the function's equation and solve for f(x).

Front

What is the domain of a function?

Back

The domain of a function is the set of all possible input values (x) 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 (f(x)) that the function can produce.

Front

What is the difference between input and output in a function?

Back

Input refers to the independent variable (x), while output refers to the dependent variable (f(x) or y) that depends on the input.

Front

What does it mean for a function to be linear?

Back

A function is linear if it can be represented by a straight line on a graph, meaning it has a constant rate of change.

Front

How can you identify a linear function from a table of values?

Back

A linear function will have a constant difference in the output values (y) for equal intervals of input values (x).

Front

What is the equation of a linear function that starts with a fixed cost and has a variable cost per unit?

Back

The equation can be expressed as Y = fixed cost + (variable cost per unit) * x.