Function and Nonfunction Flashcard

Front

What is a linear function?

Back

A linear function is a function that can be graphically represented in the Cartesian plane as a straight line. It has the form f(x) = mx + b, where m is the slope and b is the y-intercept.

Front

How can you determine if a graph represents a function?

Back

A graph represents a function if every vertical line intersects the graph at most once. This is known as the vertical line test.

Front

What is the definition of a function?

Back

A function is a relation that assigns exactly one output for each input. In other words, for every x in the domain, there is one and only one y in the range.

Front

What is a non-function?

Back

A non-function is a relation where at least one input is associated with multiple outputs. This violates the definition of a function.

Front

What does it mean for a table to represent a function?

Back

A table represents a function if each input value (x) corresponds to exactly one output value (y). If any input has more than one output, it is not a function.

Front

Evaluate f(2) if f(x) = 3x + 4.

Back

f(2) = 3(2) + 4 = 6 + 4 = 10.

Front

What is the slope-intercept form of a linear equation?

Back

The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.

Front

How do you find the value of f(x) for a given x in a linear function?

Back

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

Front

What is the significance of 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 represents the value of the function when x = 0.

Front

Evaluate g(-3) if g(x) = x^2 - 1.

Back

g(-3) = (-3)^2 - 1 = 9 - 1 = 8.