Function Basics on the SAT
Inputs, Outputs, and Domain
Build equations from context, spot patterns fast, and practice with intent.
Why the SAT Emphasizes Function Basics
A function is a promise, one input produces exactly one output. The SAT uses basic function questions to check whether you can evaluate, interpret, and respect domain restrictions.
This lesson walks you through the idea of a function as a machine, shows how to compute values from equations, tables, and graphs, and explains how to avoid giving an output for an input that is not allowed.
A Simple Definition Unlocks Function Basics
If $f(x)$ is a function, then every input $x$ has one output. You can evaluate a function by substituting a value into the rule, just as you would in any algebra expression.
The domain is the set of allowed inputs. If the function includes a denominator or square root, certain inputs may be excluded. Always check those restrictions before stating a final answer.
Work Through Function Basics Step by Step
If $f(x) = x^2 + 2x$, what is $f(3)$?
Evaluate a function by direct substitution so the input and output are clear.
Start with $f(x) = x^2 + 2x$
Compute the result to simplify the expression.
Simplify the expression to make the next step clear.
Use Desmos to Check Function Basics
If $f(x) = x^2 + 2x$, what is $f(3)$?
Desmos is useful for quick function evaluation and for checking domain restrictions by seeing where the graph exists.
f(x) = x^2 + 2x
f(3)
Algebra is faster for simple substitution. Desmos is a good check when the function is long or when you want to confirm the domain.
Desmos is faster when you need multiple function values or a quick check. Algebra is faster for a single simple evaluation.
Expert move: Define the function and evaluate it directly (for example,
f(3)), or use a table for multiple inputs; the graph shows domain restrictions
quickly.
When to skip Desmos: For a single short substitution, algebra is faster; use Desmos for long expressions or verification.
- Desmos features used: function evaluation, graphing.
- Common mistake: using an input that is not in the domain.
Practice Function Basics with SAT-Style Questions
Evaluate and interpret functions.
If , what is ?
If , which value is NOT in the domain?
From the table, what is ?
If and , what is ?
Key Takeaways to Remember for Function Basics
- A function assigns exactly one output to each input.
- Check domain restrictions before evaluating.
- Desmos helps verify values and domain quickly.
About the Instructor
