How to Evaluate Functions from a Graph

A function is one-to-one if every y value corresponds to exactly one unique x value, or if it passes the horizontal line test with each line intersecting the graph at most once.

f(-4) = 5

f(4) = 3

f(x) = -7 at x = 5

f(x) = 6 at x = 7 and x = -5

f^(-1)(7) = -6

X intercepts are at x = -1, x = 3, between x = -4 and x = 5, between x = 4 and x = 5, and between x = 6 and x = 7.

The Y intercept is at y = 4.

The domain of f(x) is from x = -6 to x = 7.

The range of f(x) is from y = -7 to y = 7.

Yes, f(x) is a function because it passes the vertical line test.

No, the inverse function is not a function because it does not pass the horizontal line test.

f(x) is not a one-to-one function because some y values have two x values.

To evaluate a function using a graph, find the corresponding point on the graph for the given x value and determine the y value at that point.

The domain is all the x values for which the function is defined, looking from left to right on the graph.

The range is all the y values for which the function is defined, looking from the bottom to the top of the graph.

The vertical line test is a method to determine if a relation is a function. If any vertical line intersects the graph at more than one point, the relation is not a function.

The horizontal line test is used to determine if a function is one-to-one. If any horizontal line intersects the graph at more than one point, the function is not one-to-one.

X intercepts are the points where the graph crosses the x-axis. To find them, look for where the graph intersects the x-axis.

The Y intercept is the point where the graph crosses the y-axis. It is found where the graph intersects the y-axis with an x value of zero.

A function is one-to-one if every y value corresponds to exactly one unique x value, or if it passes the horizontal line test with each line intersecting the graph at most once.

f(-4) = 5