Vertical line test
If any vertical line intersects a graph in more than one point, the graph does not define y as a function of x.
To find the domain of a function from the graph
Look for all the inputs on the x-axis that correspond to points on the graph. List from lowest value to highest value
To find the range of a function from the graph
Look for all the outputs on the y-axis that correspond to points on the graph. list from the lowest y-value to highest y-value.
Find increasing intervals
Look at the graph. Draw a vertical line through the points where the direction of the graph changes. Make sure the vertical line intersects the x-axis. Find the part of the graph where the y-values are increasing, but list the interval over the x-axis where this occurs.
Find decreasing intervals
Look at the graph an locate the places where the direction changes (high points or low points). Draw a vertical line through the point where direction changes. Find the part of the graph where the y-values are decreasing and list the interval from the x-axis where this occurs
When you calculate f(-x), no signs change from the original function. This means the function is even and the graph of the function is symmetric with the y-axis.
f(-x)= - f(x)
When you calculate f(-x) all of the signs become opposite of what they were. This means that the function is odd and the graph of the function is symmetric around the origin.
f(x+h) - f(x)
This is another way to calculate the slope, or rate of change
m = y2 - y1
x2 - x1