PSAT/NMSQT Prep 2022 - Eggert M.D., Strelka A. 2022

Graphs of functions
Functions
Passport to advanced math

Learning objective

After this lesson, you will be able to:

· Identify the correct graph of a function

To answer a question like this:

x	h(x)
−3	−7
−2	−5
−1	0
0	3
1	11
2	23
3	40

The minimum value of function g, whose graph is shown above, is m. Values for the function h are shown in the table above. What is the value of h(m)?

A. −7

B. −5

C. 0

D. 3

You need to know this:

Interpreting graphs of functions is similar to interpreting graphs of equations. For example:

Say the graph above represents the function f(x), and you’re asked to find the value of x for which f(x) = 6. Because f(x) represents the output value, or range, you can translate this to, “When does the y-value equal 6?” To answer the question, find 6 on the y-axis, then trace over to the function (the line). Read the corresponding x-value: it’s −2, so when f(x) = 6, x must be −2.

The PSAT may sometimes ask about a function’s maximum or minimum. These terms mean the greatest and least value of the function, respectively. This graph of f(x) does not have a maximum or minimum because the arrows on the line indicate that it continues infinitely in both directions. The preceding question, however, does show a function with a maximum.

You need to do this:

· Treat f(x) as the y-coordinate on a graph.

· The maximum and minimum refer to a function’s greatest and least y-coordinates, respectively.

Explanation:

Start by identifying m, which occurs at the lowest point of the function at (0, −3). The “minimum value of function g” means the least y-value, so m = −3. Next, use the table to find h(−3), which is the y-value for the x-value of −3. According to the table, when x = −3,h(x) = −7. Hence, (A) is correct.

Try on Your Own

Directions: Take as much time as you need on these questions. Work carefully and methodically. There will be an opportunity for timed practice at the end of the chapter.

HINT: For Q6, remember that f(x) and g(x) are found on the y-axis on the graphs.