GED Simple Functions: The Complete "How to Solve" Guide

GED Simple Functions: The Complete "How to Solve" Guide

(1,200+ words – Every line is actionable under timed conditions)

Introduction

"This question type appears 4-6 times on every GED Math test—master it, and you’ll bank 10-15 raw points, moving you from ‘Pass’ to ‘College Ready’ in one sitting."

WHAT THIS QUESTION TYPE IS ACTUALLY TESTING

The GED isn’t testing your ability to do algebra—it’s testing whether you can: 1. Translate words into math (e.g., "output is twice the input" → f(x) = 2x). 2. Spot the trap in answer choices (e.g., swapping x and y, or misapplying operations). 3. Work backward from a table/graph (e.g., "Which rule matches these inputs/outputs?").

If you treat this as a reading test with numbers, you’ll solve it faster than students who dive into calculations first.

ANATOMY OF THE QUESTION

Structure Breakdown

Representative Example Question

"The function h is defined by h(t) = 4t – 7. What is the value of h(3)?" Answer Choices: A) 5 B) 12 C) 19 D) –5

(We’ll solve this in the Worked Examples section.)

THE DECISION FRAMEWORK (Step-by-Step)

Run this process every time—no exceptions.

1. Read the stem. Circle the rule.
2. Example: "f(x) = 2x + 1" → Circle "2x + 1".

3. If no rule is given, look for a table/graph (skip to Step 4).

4. Underline the input/output variables.

5. Example: "h(t) = 4t – 7" → Underline t (input) and h(t) (output).

6. Write the rule next to the given input.

7. Example: "Find h(3)" → Write "h(3) = 4(3) – 7".

8. If given a table/graph:

9. Pick one input/output pair (e.g., x=1, y=3).
10. Test all answer choices with that pair. Eliminate wrong ones.

11. Repeat with a second pair to confirm.

12. Calculate (if needed).

13. Plug the input into the rule. Do the math in your head if possible.

14. Example: 4(3) – 7 = 12 – 7 = 5.

15. Match your answer to the choices.

16. Cross out wrong answers immediately (e.g., if you got 5, cross out B, C, D).

17. Double-check for traps.

18. Did you swap x and y? Misapply the operation? (Common traps below.)

Worked Examples

Example 1: Straightforward (Rule Given)

Question: "The function g is defined by g(x) = x² – 5. What is g(4)?" Answer Choices: A) 9 B) 11 C) 16 D) 21

Step-by-Step: 1. Circle the rule: g(x) = x² – 5. 2. Underline input/output: x (input), g(x) (output). 3. Write the rule with input: g(4) = (4)² – 5. 4. Calculate: 16 – 5 = 11. 5. Match: Choice B.

Elimination Logic: - A) 9 → 4² – 5 = 11, not 9. (Trap: forgot to square.) - C) 16 → 4² = 16, but forgot to subtract 5. - D) 21 → 4² + 5 = 21, but rule is minus 5.

Example 2: Common Trap (Table Given)

Question: "Which function matches the table?"

Answer Choices: A) f(x) = x + 2 B) f(x) = 2x + 1 C) f(x) = 3x D) f(x) = x² – 1

Step-by-Step: 1. No rule given—use the table. 2. Pick one pair: x=1, f(x)=3. 3. Test all choices with x=1:
- A) 1 + 2 = 3 ✅
- B) 2(1) + 1 = 3 ✅
- C) 3(1) = 3 ✅
- D) 1² – 1 = 0 ❌ → Eliminate D. 4. Pick a second pair: x=2, f(x)=5.
- A) 2 + 2 = 4 ❌ → Eliminate A.
- B) 2(2) + 1 = 5 ✅
- C) 3(2) = 6 ❌ → Eliminate C. 5. Only B remains.

Trap: Choice A works for x=1 but fails for x=2. Always test two pairs!

Example 3: Hard Variant (Graph Given)

Question: "The graph shows a function k. Which rule matches?" (Graph shows points: (0,2), (1,4), (2,6))

Answer Choices: A) k(x) = x + 2 B) k(x) = 2x + 2 C) k(x) = 2x D) k(x) = x² + 2

Step-by-Step: 1. Pick one point: (0,2). 2. Test all choices with x=0:
- A) 0 + 2 = 2 ✅
- B) 2(0) + 2 = 2 ✅
- C) 2(0) = 0 ❌ → Eliminate C.
- D) 0² + 2 = 2 ✅ 3. Pick a second point: (1,4).
- A) 1 + 2 = 3 ❌ → Eliminate A.
- B) 2(1) + 2 = 4 ✅
- D) 1² + 2 = 3 ❌ → Eliminate D. 4. Only B remains.

Trap: Choice D works for x=0 but fails for x=1. Graphs often include (0,y) as a distractor!

WRONG ANSWER PATTERNS

Common Mistakes

TIME STRATEGY

• Target time: 45–60 seconds per question.
• Skip if:
• The rule is complex (e.g., f(x) = (x+1)² – 3).
• You’re stuck after 90 seconds.
• Minimum work to answer confidently:
• Circle the rule/input.
• Test one input/output pair (if table/graph).
• Eliminate 2–3 wrong answers.
• Calculate only if necessary.

BACKSOLVING AND SHORTCUTS

1. Plug in x=0 first (if given a graph/table).
2. f(0) is often the y-intercept (b in y = mx + b).

3. Example: If f(0)=2, eliminate choices where f(0)≠2.

4. Use answer choices to test.

5. If the question asks "Which rule matches?", plug in x=1 for all choices first.

6. Eliminate before calculating.

7. Example: "f(x) = 5x – 2, find f(3)" → 53=15, so answer must be 15 – 2=13.

8. Cross out any choices not near 13 (e.g., 10 or 16).

9. For tables, look for patterns.

10. If x increases by 1 and y increases by 2, the rule is y = 2x + b.

1-Minute Recap

"Here’s how to solve any simple function question in under a minute:

1. Circle the rule. If it’s a table/graph, pick one input/output pair.
2. Test the easiest input first. For tables, start with x=0 or x=1. For graphs, use the y-intercept.
3. Eliminate wrong answers immediately. If a choice doesn’t match your first test, cross it out.
4. Test a second pair to confirm. Never pick an answer after just one test—traps are everywhere!
5. Double-check for swapped x/y or sign errors. Did you add when you should’ve subtracted?

This isn’t about being a math genius—it’s about following a system. Stick to these steps, and you’ll get these questions right every time. Now go practice!

FINAL TIPS FOR TEST DAY

• Write the rule on your scratch paper before calculating.
• Underline the input number (e.g., f(5)) to avoid plugging in the wrong value.
• If stuck, guess and move on. The GED rewards speed + accuracy—don’t waste time on one question.

Master this, and you’ll gain 10+ points on test day. ?