Identifying Function Graphs
Master the art of matching equations to their visual representations — a critical SAT Math skill
SAT Math
Algebra
Functions
Why Identify Function Graphs?
On the SAT, you'll need to:
- Match equations to graphs — "Which graph represents $y = 2x^2 - 3$?"
- Understand function behavior visually — increasing, decreasing, max/min
- Predict outputs — read values directly from graphs
- Analyze real-world data — population growth, projectile motion, depreciation
Key Features to Analyze:
| Shape | Line, U-curve, V-shape, S-curve, J-curve |
| Direction | Opens up/down, rises/falls, growth/decay |
| Intercepts | Where graph crosses x-axis and y-axis |
| Symmetry | About y-axis, about origin, about a line |
| End Behavior | What happens as $x \to \pm\infty$ |
| Domain & Range | Which x- and y-values exist |
⚡ Quick Identification Guide — The Master Chart
| Shape | Function Type | General Form | Key Identifier |
|---|---|---|---|
| Straight line | Linear | $y = mx + b$ | Constant rate of change |
| U-shape (smooth) | Quadratic | $y = a(x-h)^2 + k$ | Smooth curve at vertex |
| V-shape (sharp corner) | Absolute Value | $y = a|x-h| + k$ | Sharp point at vertex |
| Half-curve from a point | Square Root | $y = a\sqrt{x-h} + k$ | Starts at a point, curves one way |
| S-curve | Cubic | $y = a(x-h)^3 + k$ | Opposite end behaviors |
| J-curve with asymptote | Exponential | $y = ab^x + k$ | Rapid change, never touches asymptote |
| Two separate branches | Rational | $y = \frac{a}{x-h} + k$ | Vertical & horizontal asymptotes |