Function Representation Flashcard

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.

Front

How can you determine if a graph represents a function?

Back

Use the vertical line test: if a vertical line intersects the graph at more than one point, it does not represent a function.

Front

What is the vertical line test?

Back

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

Front

What does it mean for a set of ordered pairs to represent a function?

Back

A set of ordered pairs represents a function if no two different pairs have the same first element (input).

Front

Given the ordered pairs {(1, 2), (2, 3), (3, 4)}, does this represent a function?

Back

Yes, because each input (first element) is unique.

Front

Given the ordered pairs {(1, 2), (1, 3), (2, 4)}, does this represent a function?

Back

No, because the input '1' is associated with two different outputs (2 and 3).

Front

What is slope-intercept form of a linear equation?

Back

The slope-intercept form is given by the equation y = mx + b, where m is the slope and b is the y-intercept.

Front

How do you find the slope between two points (x1, y1) and (x2, y2)?

Back

The slope (m) is calculated using the formula m = (y2 - y1) / (x2 - x1).

Front

What is the y-intercept of a line?

Back

The y-intercept is the point where the line crosses the y-axis, represented by the value of y when x = 0.

Front

Write the equation of a line in slope-intercept form that has a slope of -2 and a y-intercept of 3.

Back

y = -2x + 3.