3.2 Characteristics of Functions

Front

What is an x-intercept in a function?

Back

An x-intercept is a point on the graph of a function where the value of y is zero. It is represented as (x, 0).

Front

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

Back

A function is increasing if, as x increases, the value of f(x) also increases. It is decreasing if, as x increases, the value of f(x) decreases.

Front

What does it mean for a function to be positive or negative?

Back

A function is positive when its output values (f(x)) are greater than zero, and negative when its output values are less than zero.

Front

What is a y-intercept in a function?

Back

A y-intercept is a point on the graph of a function where the value of x is zero. It is represented as (0, y).

Front

How do you identify the intervals where a function is increasing?

Back

To identify intervals where a function is increasing, look for sections of the graph where the slope is positive.

Front

What is the significance of the x-intercepts of a function?

Back

X-intercepts indicate the values of x for which the function equals zero, which can help in understanding the roots of the function.

Front

What does it mean for a function to be constant?

Back

A function is constant if its output value does not change as the input value changes; the graph is a horizontal line.

Front

How can you determine the overall behavior of a function from its graph?

Back

By analyzing the slopes and intercepts, you can determine if the function is increasing, decreasing, or constant over different intervals.

Front

What is the difference between local and global maxima/minima?

Back

Local maxima/minima are the highest/lowest points in a specific interval, while global maxima/minima are the highest/lowest points over the entire domain of the function.

Front

What is the role of critical points in determining the behavior of a function?

Back

Critical points are where the derivative is zero or undefined; they help identify potential local maxima, minima, or points of inflection.