Avoid Common Traps (Non-Linear Functions)

On SAT non-linear questions, most wrong answers are not “hard math.”
They’re predictable mistakes: wrong model, wrong shift direction, missing domain, percent confusion.
Fix these and your score jumps fast.

Big idea:
Traps happen when you do one of these:
solve too much
ignore restrictions
misread transformations
mix up percent vs factor

This page is a “mistake checklist” you can run before you lock in an answer.

Quick Jump (click to jump)
Use this like a pre-submit checklist

1) The Top 7 Traps (Most Frequent) If you fix these, you fix most errors	domaininside/outsidepercent
2) Trap: Wrong Function Type Quadratic vs exponential vs rational	modelkeywords
3) Trap: Missing Domain Restrictions Rationals & radicals	undefinedroot
4) Trap: Transformations (Inside/Outside) Shift direction and scaling confusion	shiftsscales
5) Trap: Percent vs Factor 1.12 vs 0.12, 0.88 vs 0.12	growthdecay
6) Trap: Equivalent Expressions Same function, different form	rewritecancel
7) SAT-Style Multiple Choice Trap-heavy questions	MCQeliminate
8) Comparison Table (Trap → Fix) Quick reference for practice	checklisttest-day

Start: Top Traps
Jump to MCQ
Jump to Trap→Fix Table
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The Top 7 Traps (Most Frequent)

If you memorize this list, you’ll catch your own mistakes before the SAT does.

Trap #1: Wrong model

“percent each year” → exponential, not linear/quadratic.

Trap #2: Missing domain restrictions

Denominator ≠ 0; inside root ≥ 0 (real numbers).

Trap #3: Inside/outside shift confusion

f(x-3) shifts right 3 (not left).

Trap #4: Percent vs multiplier

12% growth → ×1.12; 12% decrease → ×0.88.

Trap #5: Canceling without keeping restrictions

Even if factors cancel, the original restriction stays (hole).

Trap #6: Solving when you only need a feature

Often the SAT wants vertex/asymptote/intercept, not full solutions.

Trap #7: Units mismatch

“per month” vs “per year” changes the exponent and meaning.

Mini checklist (run it before final answer):
Model? Domain? Shifts correct? Percent converted? Restrictions kept? Units match?

Trap: Wrong Function Type

This is the “I solved the wrong problem” trap.

What the SAT gives you

Max/min, U-shape, area → quadratic
Percent per step, doubling/halving → exponential
Variable in denominator, undefined, asymptote → rational
Square root, endpoint, only defined after a point → radical
Distance, “at most,” V-shape → absolute value

Trap Example

“A value increases by 10% each year.”

Common wrong move:
Writing something like V=V0+0.1t (linear).

Correct model:
Multiply by 1.10 each year:

V(t)=V0(1.10)^t

Trap: Missing Domain Restrictions

The SAT loves answers that are algebraically “close” but domain-wrong.

Rational Domain Rule

If f(x)= (something)/(denominator),

then denominator ≠ 0

Trap: You simplify and forget the restriction.

Fix: Find excluded values first. Keep them even after canceling.

Hole vs Vertical Asymptote

(x^2-9)/(x-3)

=(x-3)(x+3)/(x-3)=x+3, but x≠3

Meaning: The simplified function is a line, but there’s a hole at x=3.

Radical Domain Rule

If f(x)=\u221A(inside),

then inside ≥ 0 (for real numbers)

Trap: You allow values that make the inside negative.

Quick Example

f(x)=\u221A(x-5)

Fix: x-5 ≥ 0 → x ≥ 5

Trap: Transformations (Inside vs Outside)

This is the “my graph shifts the wrong way” trap.

Inside vs Outside Rules

f(x)+k → up/down

f(x-h) → right/left

-f(x) → reflect over x-axis

f(-x) → reflect over y-axis

Trap: Thinking x-3 shifts left. (It shifts right.)

Fix: Inside shifts are “backwards.” Memorize:
x-h means right h.

Scaling Trap

f(2x) → horizontal compression

2f(x) → vertical stretch

Trap: Mixing up horizontal and vertical scaling.

Fix: Inside changes x-values; outside changes y-values.

Trap: Percent vs Multiplier

This trap destroys exponential questions.

Correct Conversions

r% increase → multiply by (1 + r)

r% decrease → multiply by (1 – r)

Remember r must be a decimal (12% = 0.12).

Trap Examples

Wrong: 15% growth → multiply by 0.15

Right: 15% growth → multiply by 1.15

Wrong: 15% decrease → multiply by 0.15

Right: 15% decrease → multiply by 0.85

Trap: Equivalent Expressions (Same Function, Different Look)

The SAT often tests equivalence more than calculation.

Equivalent ≠ same-looking

These can represent the same quadratic:

x^2 – 10x + 21

(x-3)(x-7)

(x-5)^2 – 4

Fix: Switch forms based on what the question asks:
zeros → factored; vertex → vertex form; y-intercept → standard.

Rational Equivalence Trap

(x^2-1)/(x-1) = (x-1)(x+1)/(x-1) = x+1, but x≠1

Trap: Saying domain is all real numbers.

Fix: Keep x≠1 → there’s a hole.

SAT-Style Multiple Choice (Trap-Heavy)

These are designed to trigger the exact mistakes above.

Question 1

A quantity decreases by 18% each year. If the initial value is 400, which model represents the value after t years?

400(0.18)^t
400(0.82)^t
400(1.18)^t
400 – 0.18t

Question 2

Which value is not in the domain of f(x)=(x+2)/(x-5)?

-2
0
5
7

Question 3

The graph of y=x^2 is shifted to create y=(x+4)^2.
Which transformation occurred?

Right 4
Left 4
Up 4
Down 4

Question 4

If g(x)=(x^2-1)/(x-1), which statement is true?

g(x)=x+1 for all real x
g(x)=x+1 and has a hole at x=1
g(x)=x+1 and has a vertical asymptote at x=1
g(x)=x-1 and has a hole at x=1

Question 5

The function h(x)=\u221A(x-9) is defined for:

x ≤ 9
x ≥ 9
all real x
x ≠ 9

Finisher habit:
On non-linear MCQ, after you pick an answer, do a 3-second check:
“Any domain issues? Any shift direction issues? Any percent conversion issues?”

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Trap → Fix (Quick Reference Table)

Use this while reviewing mistakes.

Trap	Fix	Fast Check
Used the wrong model type	Use keywords: percent → exponential; max/min → quadratic; denominator → rational	Ask: “What’s the signal word?”
Forgot domain restrictions	Write restrictions first: denom ≠ 0; inside root ≥ 0	Ask: “Any x-values not allowed?”
Shifted the wrong way	Inside shifts are “backwards”: x-h means right h	Check the anchor (vertex/corner/endpoint)
Percent used as 0.12 instead of 1.12	Growth: multiply by 1+r; Decay: multiply by 1-r	Ask: “Is my multiplier near 1?”
Canceled factors and lost the hole	Keep original restriction even after simplifying	Ask: “Did anything cancel?”
Solved too much	Read features instead (vertex, intercepts, asymptotes)	Ask: “Do I only need a feature?”
Units mismatch in exponent	Match t to the time unit (“per month” vs “per year”)	Ask: “What is one step?”

Bottom line:
Most SAT non-linear mistakes are predictable. If you can catch them, you can prevent them.
That’s one of the fastest ways to increase your score.

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