Domain: in a graph, the domain is on the x-axis [x = ?]
Range: in a graph, the range is on the y-axis [y = ?]

RULES 1 FOR FUNCTION PROBLEMS (GRAPHS)
To identify whether a graph belongs to a function, you can use the “pencil test”. That is, hold your pencil vertically and move it across the x-axis. If the pencil intersects the graph at only one point, then the graph represents a function.

If you take your pencil and move it horizontally across the graph on the left, you will find that the pencil intersects the graph at only one point. Thus the graph represents a function.

RULES 2 FOR FUNCTION PROBLEMS (GRAPHS)

In this type of question, you will be given a function and its corresponding graph. Then you will be given a new function and asked to identify the graph of the new function. First, you must identify whether the value changes for the x-coordinates, the y-coordinates, or both. Once you have identified the value changes, you can apply the following rules.

If the New Function…                        Then the Graph…

Adds to the x-value                                Shifts to the left

Subtracts from the x-value                    Shifts to the right

Adds to the y-value                                Shifts upwards

Subtracts from the y-value                    Shifts downwards

SAMPLE PRACTICE QUESTION FOR FUNCTIONS (GRAPHS)

The graph of y = s(a) is pictured above. If s(7) = p, then what is one possible value of g(p)?

     Solution
     1) First, s(7) = p gives an x-value of 7.
         When the x-coordinate = 7 in the graph, the y-coordinate = 4.
         Therefore, s(7) = p = 4.

     2) Next, take s(p). Since p = 4, it can be written as s(4). This gives an x-value of 4.

     3) When the x-coordinate = 4 in the graph, the y-coordinate = 3. Thus s(p) = 3.

SAT Math: Function Graphs and Shifts Practice

Lesson Includes:

—Math Terms for Function Graphs and Shifts

—Rules for Function Graphs and Shifts Problems

—Sample Practice Questions

—Practice Questions

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