1.1 - 1.2 Practice

Front

What is an increasing interval in a function?

Back

An increasing interval is a range of x-values where the function's output (f(x)) rises as x increases.

Front

What is a decreasing interval in a function?

Back

A decreasing interval is a range of x-values where the function's output (f(x)) falls as x increases.

Front

What does it mean when a function is constant on an interval?

Back

A function is constant on an interval if its output (f(x)) does not change as x varies within that interval.

Front

How can you determine if a function is increasing or decreasing on an interval?

Back

You can determine this by analyzing the slope of the function's graph: if the slope is positive, the function is increasing; if negative, it is decreasing.

Front

What is the significance of critical points in a function?

Back

Critical points are where the function's derivative is zero or undefined, indicating potential local maxima, minima, or points of inflection.

Front

What is the derivative of a function?

Back

The derivative of a function represents the rate of change of the function's output with respect to its input, often interpreted as the slope of the tangent line to the graph.

Front

What does it mean for a function to have a positive interval?

Back

A positive interval is a range of x-values where the function's output (f(x)) is greater than zero.

Front

What does it mean for a function to have a negative interval?

Back

A negative interval is a range of x-values where the function's output (f(x)) is less than zero.

Front

How do you identify the intervals of increase and decrease from a graph?

Back

You can identify intervals of increase and decrease by observing the direction of the graph: rising indicates increasing, while falling indicates decreasing.

Front

What is the relationship between the first derivative and the behavior of a function?

Back

The first derivative indicates the function's increasing or decreasing behavior: f'(x) > 0 means increasing, f'(x) < 0 means decreasing.