Flashcard 5 - Graphs and Functions

Front

What is a function in mathematics?

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 does the term 'domain' refer to in a function?

Back

The domain of a function is the complete set of possible values of the independent variable (input) for which the function is defined.

Front

What does the term 'range' refer to in a function?

Back

The range of a function is the complete set of possible values of the dependent variable (output) that results from using the function.

Front

How do you determine if a function is increasing?

Back

A function is increasing on an interval if, as the input values increase, the output values also increase.

Front

What does a decreasing function look like on a graph?

Back

A decreasing function slopes downward from left to right, indicating that as the input increases, the output decreases.

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 the y-coordinate divided by the change in the x-coordinate (rise/run).

Front

What does it mean for a graph to represent a real-world situation?

Back

A graph represents a real-world situation when it visually depicts relationships between variables in a context that can be understood and analyzed.

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 y = mx + b, where m is the slope and b is the y-intercept.

Front

How can you find the range of a function given its domain?

Back

To find the range, substitute each value from the domain into the function and determine the corresponding output values.

Front

What does it mean for a graph to have a section that is flat?

Back

A flat section of a graph indicates that the output value remains constant as the input value changes, meaning the function is neither increasing nor decreasing.