Daily Regents: Graphing and Translating Absolute Value (August 2014)

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)

Any questions?

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