To find the domain of a function from its graph...
To find the range of a function from its graph...
To approximate the relative minimum or maximum of a function using a graphing utility,...
Let a(,f(a)) and (b,f(b)) be two points on the graph of a nonlinear function f. The average rate of change of f from a to b is given by:
[f(b) - f(a)]/(b - a)
is the average rate of change of f(x) from a to b.
To find the domain of a function from its graph:
1. Look at the x-values (horizontal axis) of the graph.
2. Identify the values of x for which the graph is defined, meaning there are no gaps or breaks in the graph.
3. The domain of the function is the set of all x-values for which the graph exists. It may be a specific interval or the set of all real numbers.
To find the range of a function from its graph:
1. Look at the y-values (vertical axis) of the graph.
2. Identify all the possible values that the graph takes on.
3. The range of the function is the set of all y-values that the graph can reach. It may be a specific interval or the set of all real numbers.
To approximate the relative minimum or maximum of a function using a graphing utility:
1. Plot the graph of the given function using a graphing utility.
2. Identify the points on the graph where the function reaches local maximum or minimum values.
3. These points will appear as high or low points on the graph, respectively.
4. The x-coordinate of the high or low point represents the value of x where the relative maximum or minimum occurs.
5. The y-coordinate of the high or low point represents the corresponding value of the function f(x) at that point.
The average rate of change of f from a to b is given by:
The average rate of change is calculated as the difference in the function values divided by the difference in the corresponding x-values.
Average Rate of Change = (f(b) - f(a))/(b - a)