Key Features of Functions

Front

What are the x- and y-intercepts of a function?

Back

The x-intercepts are the points where the function crosses the x-axis (y=0), and the y-intercept is the point where the function crosses the y-axis (x=0).

Front

How do you find the x-intercepts of a function?

Back

Set the function equal to zero and solve for x. The solutions are the x-intercepts.

Front

How do you find the y-intercept of a function?

Back

Evaluate the function at x=0. The result is the y-intercept.

Front

What is end behavior in the context of functions?

Back

End behavior describes how the values of a function behave as x approaches positive or negative infinity.

Front

Back

It means that as x increases without bound, the function's values decrease towards negative infinity.

Front

Back

It means that as x decreases without bound, the function's values increase towards positive infinity.

Front

How do you determine where a function is increasing or decreasing?

Back

Analyze the first derivative of the function. If the derivative is positive, the function is increasing; if negative, it is decreasing.

Front

What is the domain of a function?

Back

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

Front

What is the range of a function?

Back

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

Front

How do you identify the domain of a polynomial function?

Back

The domain of a polynomial function is all real numbers, or (-∞, ∞).