Domain 3: 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.

Tags

CCSS.8.F.A.1

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 find the average rate of change of a function between two points?

Back

The average rate of change of a function between two points (x1, y1) and (x2, y2) is calculated as \( \frac{y_2 - y_1}{x_2 - x_1} \).

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6

Front

What is a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically in the form \( f(x) = ax^2 + bx + c \), where a, b, and c are constants.

Front

What does the vertex of a parabola represent in a quadratic function?

Back

The vertex of a parabola represents the maximum or minimum point of the quadratic function, depending on the direction of the parabola.

Front

What is the significance of the y-intercept in a 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 is zero.

Front

What is a linear function?

Back

A linear function is a function that graphs to a straight line and 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

How do you determine if a relation is a function?

Back

A relation is a function if every input value corresponds to exactly one output value, which can be checked using the vertical line test.

Tags

CCSS.8.F.A.1

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, calculated as \( \frac{\text{rise}}{\text{run}} \) or the change in y over the change in x.

Tags

CCSS.8.EE.B.5