Advanced Math • 35% of test
Function Notation
Select your difficulty level to start practicing. We recommend mastering each level before moving to the next.
Beginner5 Sets
Beginner Practice
Start here to build your foundation. Clear problems and straightforward calculations.
Target Score
400-550
Intermediate5 Sets
Intermediate Practice
Level up with more complex equations and multi-step problems.
Target Score
550-700
Advanced3 Sets
Advanced Practice
Master the hardest concepts. Complex word problems and abstract applications.
Target Score
700-800
What is Function Notation?
Function notation (f(x)) describes input-output relationships. The SAT tests evaluating functions, composing functions, and understanding transformations.
Step-by-Step Strategy
⚠️ Common Traps to Avoid
Frequently Asked Questions
What does f(3) mean?
Find the output when the input is 3. Substitute 3 for x in the function rule.
How do I compose functions?
For f(g(x)), evaluate from inside out. First find g(x), then use that value in f.
What's the difference between f(x)+2 and f(x+2)?
f(x)+2 shifts the graph UP 2 units. f(x+2) shifts the graph LEFT 2 units.
How do I find where f(x) = 3?
Set the function equal to 3 and solve for x. This finds which input gives output 3.
What is domain?
All possible input values. Watch for values that cause division by zero or negative square roots.
Are function questions common?
Yes, function notation appears throughout the test. Master these basics in our <a href='/math'>comprehensive Math section</a>.
How do I find the 'Inverse' of a function f(x)?
1) Replace f(x) with y, 2) Swap x and y, 3) Solve for the new y. The result is the inverse f⁻¹(x).
What is the 'Vertical Line Test'?
A curve is a function if every vertical line crosses the graph at most once. It ensures each input has exactly one output.
How do I evaluate a piecewise function?
Check which condition the input x satisfies, then plug that x into ONLY that specific part of the function definition.
What does f(g(h(x))) mean?
This is triple composition. Work from the innermost function outward: first calculate h(x), then g(that result), then f(final result).
What is an 'Even Function'?
A function where f(-x) = f(x). Its graph is symmetric across the y-axis (like y = x² or y = cos(x)).
What is an 'Odd Function'?
A function where f(-x) = -f(x). Its graph has rotational symmetry around the origin (like y = x³ or y = sin(x)).
How do I interpret f(x) = g(x) on a graph?
These are the x-coordinates of the points where the two graphs intersect. It's where the functions share the same output.
What is 'Average Rate of Change' in function terms?
It's the slope of the secant line between two points: [f(x₂) - f(x₁)] / [x₂ - x₁]. For linear functions, it's just the slope m.
Can a function have more than one y-intercept?
No. By definition, each input (x=0) can have ONLY one output. Master mapping in our <a href='/math/functions/intermediate'>Intermediate Functions practice</a>.