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.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

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).

Tags

CCSS.8.EE.B.5

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).

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

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.

Tags

CCSS.8.F.A.1

CCSS.HSF.IF.A.1

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.

Tags

CCSS.8.F.A.3

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).

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

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.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2