Functions as Equations flashcard

Front

What is a function?

Back

A function is a relation that assigns exactly one output for each input. In other words, for every input value (x), there is one and only one output value (f(x)).

Tags

CCSS.8.F.A.1

Front

How do you evaluate a function at a specific point?

Back

To evaluate a function at a specific point, substitute the value of the variable into the function's equation. For example, if f(x) = 2x + 1, to find f(1), substitute 1 for x: f(1) = 2(1) + 1 = 3.

Tags

CCSS.HSF.IF.A.2

Front

What does it mean for a relation to be a function?

Back

A relation is a function if each input value corresponds to exactly one output value. This means no two ordered pairs can have the same first element (input).

Tags

CCSS.8.F.A.1

Front

What is an ordered pair in the context of functions?

Back

An ordered pair is a pair of numbers (x, y) that represents a point on a graph, where x is the input and y is the output of a function.

Tags

CCSS.8.F.A.1

CCSS.HSF.IF.A.1

Front

What is the vertical line test?

Back

The vertical line test is a method to determine if a graph represents a function. If any vertical line intersects the graph at more than one point, the graph does not represent a function.

Front

What is the difference between independent and dependent variables?

Back

The independent variable is the input of a function (often x), while the dependent variable is the output (often y) that depends on the value of the independent variable.

Tags

CCSS.6.EE.C.9

Front

How can you convert a function notation to a coordinate point?

Back

To convert a function notation like g(15) = -1 to a coordinate point, write it as (15, -1), where 15 is the input and -1 is the output.

Tags

CCSS.8.F.A.1

CCSS.HSF.IF.A.1

Front

What is a mapping diagram?

Back

A mapping diagram visually represents a function by showing how each input is paired with its corresponding output. It helps to illustrate whether a relation is a function.

Tags

CCSS.8.F.A.1

Front

What does it mean for a function to be linear?

Back

A linear function is a function that can be graphically represented as a straight line. Its general form is 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 is the slope of a line?

Back

The slope of a line is a measure of its steepness, calculated as the change in y divided by the change in x (rise/run). It indicates how much y changes for a unit change in x.

Tags

CCSS.8.EE.B.5