Analyzing Graphs and Identifying Functions

Front

What is a function in mathematics?

Back

A function is a relation where each input (x-value) has exactly one output (y-value).

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 is not a function.

Front

What does it mean for a graph to increase at a constant rate?

Back

It means that for equal increments of x, the y-values increase by the same amount.

Front

What does it mean for a graph to decrease at a constant rate?

Back

It means that for equal increments of x, the y-values decrease by the same amount.

Front

What is the significance of the x-values in a function?

Back

In a function, each x-value must be unique; no x-value can correspond to more than one y-value.

Front

What is a linear function?

Back

A linear function is a function that graphs to a straight line, represented by the equation y = mx + b.

Front

What is a non-linear function?

Back

A non-linear function is a function that does not graph to a straight line, such as quadratic or exponential functions.

Front

What is the domain of a function?

Back

The domain is the set of all possible input values (x-values) for the function.

Front

What is the range of a function?

Back

The range is the set of all possible output values (y-values) for the function.

Front

What is a constant function?

Back

A constant function is a function that does not change; it has the same output for every input.