Basic Functions in Math

Front

What is a function in mathematics?

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.

Tags

CCSS.8.F.A.1

Front

What is the definition of slope in a linear function?

Back

The slope is a measure of the steepness of a line, calculated as the change in the y-coordinate divided by the change in the x-coordinate (rise over run).

Tags

CCSS.8.EE.B.5

Front

How can you determine if a mapping is a function?

Back

A mapping is a function if every input (x-value) has exactly one output (y-value). If any input is associated with more than one output, it is not a function.

Tags

CCSS.8.F.A.1

Front

What are independent and dependent variables in a function?

Back

Independent variables are the inputs of a function (often represented as x), while dependent variables are the outputs (often represented as y) that depend on the independent variables.

Front

What does it mean for a function to be linear?

Back

A linear function is a function that graphs to a straight line and can be expressed in the form y = 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 is the y-intercept of a linear function?

Back

The y-intercept is the point where the line crosses the y-axis, which occurs when x = 0.

Front

How do you find the slope from two points on a line?

Back

The slope (m) can be calculated using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points.

Tags

CCSS.8.EE.B.5

Front

What is the standard form of a linear equation?

Back

The standard form of a linear equation is Ax + By = C, where A, B, and C are integers, and A should be non-negative.

Front

What is the difference between a function and a relation?

Back

A relation is any set of ordered pairs, while a function is a specific type of relation where each input is associated with exactly one output.

Tags

CCSS.8.F.A.1

Front

What is a vertical line test?

Back

The vertical line test is a method used to determine if a curve is a function. If any vertical line intersects the curve more than once, it is not a function.