Characteristics of Functions

Front

What is the range of a function?

Back

The range of a function is the set of all possible output values (y-values) that the function can produce based on its domain.

Front

What is the domain of a function?

Back

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

Front

What are x-intercepts?

Back

X-intercepts are the points where the graph of a function crosses the x-axis, meaning the output value (y) is zero.

Front

How do you determine where a function is positive?

Back

A function is positive where its output values (y) are greater than zero. This can be found by analyzing the graph or solving the function.

Front

What does it mean for a function to be increasing?

Back

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

Front

What does it mean for a function to be decreasing?

Back

A function is decreasing on an interval if, as the input values (x) increase, the output values (y) decrease.

Front

What is a 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, it is not a function.

Front

What is a constant function?

Back

A constant function is a function that always returns the same value, regardless of the input. Its graph is a horizontal line.

Front

What is a linear function?

Back

A linear function is a function that can be expressed in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What is a quadratic function?

Back

A quadratic function is a function that can be expressed in the form y = ax² + bx + c, where a, b, and c are constants and a ≠ 0.