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.
