Master SAT function notation and behavior with this 10-question set, focusing on evaluating functions, interpreting graphs, finding roots, and analyzing linear/quadratic function transformations.
Functions Tips & Tricks
A function is a rule.
It takes an input and gives exactly one output.
If one input gives two different outputs, it is not a function.
Know the parts.
Input = usually x
Output = usually y or f(x)
f(x) means “the value of the function when x is plugged in”
Treat f(x) like y.
If you see
f(x) = 2x + 3
that just means the output is found by using the rule 2x + 3.
Plug in carefully.
If f(x) = 3x − 4, then
f(2) = 3(2) − 4 = 2
Parentheses matter.
If f(x) = x² + 1, then
f(-3) = (-3)² + 1 = 10
not -8
Watch for function notation traps.
f(2) means plug in 2
2f(x) means multiply the entire function by 2
Those are not the same thing.
Tables can show functions too.
A table is a function if each input appears only once with one output.
Graphs: use the vertical line test.
If a vertical line hits the graph more than once, it is not a function.
Common SAT function jobs include:
plugging in values
finding output
comparing functions
interpreting graphs/tables
finding rate of change
writing equations from patterns
Know function transformations.
f(x) + 3 = shift up
f(x) − 2 = shift down
f(x + 4) = shift left
f(x − 5) = shift right
Inside changes and outside changes are different.
outside changes affect y
inside changes affect x
Look for what the question is really asking.
Many function questions look hard because of notation, but really they are just asking:
plug in a value
read a graph
compare outputs
identify the rule
For word problems, connect the variables.
Ask:
what is the input?
what is the output?
what does the function represent?
Rate of change matters.
In linear functions, the coefficient of x is the slope, or how fast the output changes.
Do not panic when functions look abstract.
Most SAT function questions are really about:
substitution
patterns
interpretation
careful reading
Quick shortcut
Before solving, ask:
What is the input, what is the rule, and what output do they want?
Final reminder
Functions are just input-output rules.
If you can identify the input, apply the rule carefully, and keep the notation straight, most function questions become much easier.