*I'll be reviewing a*

**New York State Regents Exam**Question every day from now until the Regents exams begin next month. At least, that is the plan.### August 2014, Questions 33

**33.** *
On the axes below, graph f(x) = |3x|.
If g(x) = f(x) - 2, how is the graph of f(x) translated to form the graph of g(x)?
If h(x) = f(x - 4), how is the graph of f(x) translated to form the graph of h(x)?
*

You can use the graphing calculator to see what the function looks like. Press the **MATH** key, and then arrow over to the **NUM** menu and *abs(* will be the first option. Depending on your calculator's operating system, you will either get **abs(** written as a function, or you will see the symbols: **| |**

If you have the symbols, put the variable between them. If you have the function, add the variable and then *close the parentheses!* This will be important later in the problem.

g(x) will translate the function 2 spaces down. If you subtract two from a number after taking the square root, the value will always decrease by 2. Example: f(0) = 0, g(0) = 0 - 2 = -2.

h(x) will translate the function 4 spaces to the right. Taking the absolute value after subtracting means that any negative results will become positive. Example f(0) = 0, h(0) = f(0-4) = 4, but f(4) = 4, h(4) = f(4-4) = 0. The vertex of the function has shifted four places to the right.

You can look at the graphs of g(x) and h(x) in the calculator to compare.
* Remember:* if your calculator's operating system shows

*abs(*for absolute value, you must close the parentheses:

**y = abs(x) - 2**

y = abs(x - 4)

y = abs(x - 4)

Any questions?

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