Analyzing Functions & Graphs

Front

What does it mean for a function to be increasing?

Back

A function is increasing on an interval if, as the input values (x) increase, the output values (f(x)) also increase.

Front

What does it mean for a function to be decreasing?

Back

A function is decreasing on an interval if, as the input values (x) increase, the output values (f(x)) decrease.

Front

What is a constant function?

Back

A constant function is a function that does not change its value; it remains the same regardless of the input.

Front

How can you determine if a function is increasing or decreasing from its graph?

Back

You can determine if a function is increasing or decreasing by observing the slope of the graph: if the graph rises from left to right, it is increasing; if it falls, it is decreasing.

Front

What is the definition of a function?

Back

A function is a relation that assigns exactly one output value for each input value.

Front

What is the domain of a function?

Back

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

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.

Front

What is a linear function?

Back

A linear function is a function that graphs to a straight line and can be expressed in the form f(x) = mx + b, where m is the slope and b is the y-intercept.

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, calculated as the change in y (rise) divided by the change in x (run).

Front

What is a quadratic function?

Back

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