Key Features of Functions

Front

What are the zeros of a function?

Back

The zeros of a function are the values of x for which the function f(x) = 0. For example, if f(x) = x^2 - 4, the zeros are x = 2 and x = -2.

Front

What does it mean for a graph to be decreasing?

Back

A graph is decreasing on an interval if, as x increases, the value of f(x) decreases. For example, if a graph goes down from left to right on the interval (-∞, 3), it is decreasing there.

Front

What is an interval in mathematics?

Back

An interval is a range of numbers between two endpoints. It can be open (not including endpoints) or closed (including endpoints). For example, [-3, -1] is a closed interval.

Front

What is the range of a function?

Back

The range of a function is the set of all possible output values (f(x)) that the function can produce. For example, if f(x) = x^2, the range is [0, ∞) because the output is always non-negative.

Front

How do you determine where a graph is constant?

Back

A graph is constant on an interval if the value of f(x) does not change for all x in that interval. For example, if f(x) = 5 for x in [-3, -1], the graph is constant there.

Front

What does it mean for a graph to be constant?

Back

A graph is constant if it does not rise or fall; it remains at the same value across an interval. For example, a horizontal line represents a constant function.

Front

What is the difference between an open and closed interval?

Back

An open interval (a, b) does not include the endpoints a and b, while a closed interval [a, b] includes both endpoints.

Front

What is the significance of the vertex in a quadratic function?

Back

The vertex of a quadratic function is the highest or lowest point on the graph, depending on whether it opens upwards or downwards. It represents the maximum or minimum value of the function.

Front

How can you find the zeros of a quadratic function?

Back

You can find the zeros of a quadratic function by factoring, using the quadratic formula, or by graphing the function and identifying where it crosses the x-axis.

Front

What does it mean for a function to be increasing?

Back

A function is increasing on an interval if, as x increases, the value of f(x) also increases. For example, if a graph goes up from left to right on the interval (3, ∞), it is increasing there.