Function Characteristics Practice 1

Front

What is the end behavior of a function?

Back

The end behavior of a function describes how the function behaves as the input values (x) approach positive or negative infinity. It indicates the direction in which the graph of the function moves at the extremes.

Front

What does it mean for a mapping diagram to represent a function?

Back

A mapping diagram represents a function if each input (x-value) is paired with exactly one output (y-value). If any input is paired with more than one output, it is not a function.

Front

How do you find 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. To find the domain, identify any restrictions such as division by zero or square roots of negative numbers.

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 does it mean for a function to be continuous?

Back

A function is continuous if there are no breaks, jumps, or holes in its graph. This means that for every x-value in the domain, there is a corresponding y-value.

Front

What is the difference between a function and a relation?

Back

A relation is any set of ordered pairs, while a function is a specific type of relation where each input is associated with exactly one output.

Front

How can you determine if a graph represents a function?

Back

You can use the vertical line test: if a vertical line intersects the graph at more than one point, then the graph does not represent a function.

Front

What is an asymptote?

Back

An asymptote is a line that a graph approaches but never touches. It can be vertical, horizontal, or oblique.

Front

What is the significance of the y-intercept in a function?

Back

The y-intercept is the point where the graph of the function crosses the y-axis. It represents the output value when the input value (x) is zero.

Front

What is a polynomial function?

Back

A polynomial function is a function that can be expressed in the form f(x) = a_n*x^n + a_(n-1)*x^(n-1) + ... + a_1*x + a_0, where a_n, a_(n-1), ..., a_0 are constants and n is a non-negative integer.