Algebra
Tackling Obey the Function!
Rebels don’t get functions items right, so take a break from the “down with the establishment” routine when you encounter any function items. Check out the following step method:
Step 1: Determine what kind of function item you have.
Step 2: If there’s an input number, run it through the function.
Step 3: Determine whether another number needs to be run through the function or whether one go-through is enough.
Ok. Time to practice.
Obey the Function! in Slow Motion
6. Let the operation be defined such that . What is the result of (7)?
(A) –11
(B) –8
(C) 8
(D) 11
(E)
Step 1: Determine what kind of function item you have.
Just to make things a bit cutesy, we gave you a function item that portrays two different types of functions. It’s got a weird symbol, although that weird symbol could be exchanged for an f(x) and nothing would really change. It’s also a compound function, because you have to run the function twice.
Step 2: If there’s an input number, run it through the function.
That’s just what we’ll do with the inner, nested function. First, we plug in 7 for r:
Step 3: Determine whether another number needs to be run through the function or whether one go-through is enough.
Like a badly soiled shirt, this item needs another washing in our function machine. This time, we’ll plug in –8 for r:
There’s your answer, A. So long as you do as you’re told, functions won’t give you any trouble.
Guided Practice
Try this item on your own.
7. Which of the following provides the best description of the events shown in the above graph?
(A) Sales rose steadily in the 1970s, faltered badly in the 1980s, then started recovering in the 1990s.
(B) Sales were stable in the 1970s, dropped in the 1980s, then rose in the 1990s.
(C) Sales remained flat during the 1970s and increased over the next 10 years but have been falling ever since.
(D) Sales rose in the 1980s, fell over the next 10 years, then remained stable.
(E) Sales increased during the 1980s, dropped sharply during the 1990s, then began recovering again in the 2000s.
Step 1: Determine what kind of function item you have.
With the presence of a graph, the answer should come to you. Review the different types of functions on page if you’re not sure.
Step 2: If there’s an input number, run it through the function.
This is the only type of function that doesn’t require the grinding of numbers. In a sense, the numbers have been ground and are already on display.
Step 3: Determine whether another number needs to be run through the function or whether one go-through is enough.
A run-through of the answer choices and a comparison to the graph is what is needed.
Guided Practice: Explanation
Step 1: Determine what kind of function item you have.
This is a Function as Model item. There is a slight chance the graph would throw you off and make you think it is a graphed function, but the answer choices and stem should dispel any notion of that.
Step 2: If there’s an input number, run it through the function.
The new SAT added a wrinkle to the old function item. In this instance, you have to obey the function by looking at the chart and finding the answer choice that follows what the chart depicts. We’re looking for flat sales in the 1970s, an increase in the 1980s, a decrease in the 1990s, and another increase in the 2000s.
Step 3: Determine whether another number needs to be run through the function or whether one go-through is enough.
A quick read-through of the answer choices is enough for us to conclude that E is the correct answer.
Independent Practice
After you complete the following item, look at the following page for the explanation.
5. If , then what is the value of ?
(A) 512
(B) 251
(C) 128
(D) –10
(E) –261
Independent Practice: Explanation
Step 1: Determine what kind of function item you have.
This is a pretty straightforward function item. The only catch here is that you have to subtract one function from another.
Step 2: If there’s an input number, run it through the function.
Let’s input our first number, 4, into the function and see what happens:
Lovely.
Step 3: Determine whether another number needs to be run through the function or whether one go-through is enough.
Now let’s run through the function with –4:
There’s your answer, E, right? Wrong! The stem asks you for , so you need to take the two values you came up with and subtract: , answer choice A.
Help | Feedback | Make a request | Report an error