Domain, Range, and Graph Features
Key vocabulary and strategies for describing a function's inputs, outputs, and graph shape on the PSAT.
Keyboard Shortcuts
💡 Pro tip: Use keyboard shortcuts for faster studying!
Study Smart Tips for Domain, Range, and Graph Features
Master these concepts using proven study techniques that actually work:
Active Recall
Test yourself before flipping each card to strengthen memory retention
Spaced Repetition
Review difficult cards more frequently than easy ones
Multiple Sessions
Break study time into shorter, focused sessions
Explain Aloud
Verbalize answers to reinforce understanding
Questions Covered in This Set
10 cards to master
What is the domain of a function?
The set of all allowed inputs (x-values). On a graph it's the horizontal span.
What two algebraic situations usually restrict a domain?
Division by zero (denominator can't be 0) and square roots of negatives (radicand must be ≥ 0).
Domain of g(x) = √(x − 9)?
x − 9 ≥ 0, so x ≥ 9.
What is the range of a function?
The set of all outputs (y-values) the function actually produces — the vertical span of the graph.
Range of f(x) = (x − 3)² − 5?
y ≥ −5, because the vertex (3, −5) is the minimum point.
How do you decide where a function is increasing or decreasing?
Read the graph left to right: uphill = increasing, downhill = decreasing, flat = constant. Describe with x-intervals.
What is a zero of a function?
An input where the output is 0 — also called a root or x-intercept. Solve f(x) = 0.
Difference between a zero and the y-intercept?
A zero is where y = 0 (set f(x)=0); the y-intercept is f(0), the output when x = 0.
In a profit model P(x), what does a zero mean?
A break-even point — where profit is exactly $0.
For h(t) = −16t² + 64t, find the zeros, max height, and realistic domain.
Zeros t = 0 and t = 4; max at t = 2 with h(2) = 64 ft; realistic domain 0 ≤ t ≤ 4, range 0 ≤ h ≤ 64.
