NC.M1.F-IF.4: Interpret functions in context

Front

What is a function in mathematics?

Back

A function is a relation that assigns exactly one output (y) for each input (x).

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.

Front

What does it mean for a function to be decreasing?

Back

A function is decreasing on an interval if, as x increases, the value of f(x) decreases.

Front

What is the vertex of a parabola?

Back

The vertex is the highest or lowest point of a parabola, depending on its orientation.

Front

How do you determine the maximum height of a projectile?

Back

The maximum height can be found by calculating the vertex of the quadratic function that models the height.

Front

What is the significance of the x-intercept in a height vs. time graph?

Back

The x-intercept represents the time when the object reaches the ground (height = 0).

Front

What is a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically in the form f(x) = ax^2 + bx + c.

Front

What does the term 'interval' refer to in mathematics?

Back

An interval is a range of values between two endpoints, often expressed in the form [a, b] or (a, b).

Front

What is the difference between a closed interval and an open interval?

Back

A closed interval includes its endpoints, while an open interval does not.

Front

How can you identify the interval where a function is increasing or decreasing from a graph?

Back

By observing the slope of the graph; if the graph rises, the function is increasing, and if it falls, the function is decreasing.