58 Rational Key Features

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. For example, the range of the function f(x) = x^2 is [0, ∞) because it can only produce non-negative values.

Front

What is the domain of a function?

Back

The domain of a function is the set of all possible input values (x-values) that the function can accept. For example, the domain of the function f(x) = 1/x is all real numbers except x = 0.

Front

What does it mean for a function to have end behavior?

Back

End behavior describes how the values of a function behave as the input approaches positive or negative infinity. It helps to understand the overall trend of the function.

Front

What is the end behavior on the left for the function f(x) = x^2?

Back

As x approaches -∞, f(x) approaches ∞.

Front

What is the end behavior on the right for the function f(x) = x^2?

Back

As x approaches ∞, f(x) approaches ∞.

Front

What is a rational function?

Back

A rational function is a function that can be expressed as the ratio of two polynomials. For example, f(x) = (x^2 + 1)/(x - 1) is a rational function.

Front

What is a vertical asymptote?

Back

A vertical asymptote is a line x = a where a function approaches infinity or negative infinity as x approaches a. It indicates that the function is undefined at that point.

Front

What is a horizontal asymptote?

Back

A horizontal asymptote is a line y = b that a function approaches as x approaches infinity or negative infinity. It indicates the value that the function approaches at the extremes.

Front

What is the significance of the x-intercept?

Back

The x-intercept of a function is the point where the graph of the function crosses the x-axis. It represents the value of x when f(x) = 0.

Front

What is the significance of the y-intercept?

Back

The y-intercept of a function is the point where the graph of the function crosses the y-axis. It represents the value of f(x) when x = 0.