Comparing Functions - Flashcard

Front

What is the rate of change in a linear function?

Back

The rate of change in a linear function is the ratio of the change in the output value (y) to the change in the input value (x), often represented as the slope (m) in the equation y = mx + b.

Front

How do you determine if a table represents a linear relationship?

Back

A table represents a linear relationship if the differences between consecutive y-values divided by the differences between consecutive x-values are constant.

Front

What does it mean if two functions have the same rate of change?

Back

If two functions have the same rate of change, it means they increase or decrease at the same rate, resulting in parallel lines when graphed.

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 horizontal line test?

Back

The horizontal line test is used to determine if a function is one-to-one. If any horizontal line intersects the graph at more than one point, the function is not one-to-one.

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

What is the definition of a linear function?

Back

A linear function is a function that can be graphically represented as a straight line, described by the equation y = mx + b, where m is the slope and b is the y-intercept.

Front

What does it mean for an equation to be a function?

Back

An equation is a function if for every input (x-value), there is exactly one output (y-value).

Front

What is the slope of a line?

Back

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

Front

How can you find the slope from a graph?

Back

To find the slope from a graph, select two points on the line, calculate the rise (difference in y-coordinates) and the run (difference in x-coordinates), and divide rise by run.