Analyzing Functions

Front

What does it mean for a function f(x) to be positive?

Back

A function f(x) is positive when its output values are greater than zero, meaning the graph of the function lies above the x-axis.

Front

How do you determine the intervals where f(x) is positive?

Back

To find where f(x) is positive, identify the x-values for which the function's output is greater than zero by analyzing the graph or solving the inequality.

Front

What is an increasing function?

Back

An increasing function is one where, as the input x increases, the output f(x) also increases.

Front

How can you identify the intervals where a function is increasing on a graph?

Back

Look for sections of the graph where the slope is positive; these are the intervals where the function is increasing.

Front

What does it mean for a function to be decreasing?

Back

A function is decreasing when, as the input x increases, the output f(x) decreases.

Front

How do you find the intervals where a function is decreasing?

Back

Identify sections of the graph where the slope is negative; these intervals indicate where the function is decreasing.

Front

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

Back

The x-intercepts are the points where the function crosses the x-axis, indicating the values of x for which f(x) = 0.

Front

What is the role of the y-intercept in a function?

Back

The y-intercept is the point where the function crosses the y-axis, representing the value of f(x) when x = 0.

Front

What does it mean for a function to have a maximum value?

Back

A maximum value is the highest point on the graph of the function, where the function reaches its peak before decreasing.

Front

What does it mean for a function to have a minimum value?

Back

A minimum value is the lowest point on the graph of the function, where the function reaches its lowest point before increasing.