Function Launch Worksheet
Daily Warm-Up Algebra 1 • Function Notation
Function Evaluation Launch
Target Time: 5–8 Min
Order of Operations Focus
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Key Concept: In function notation \( g(x) \), the value inside the parentheses replaces the input variable \( x \). Use standard order of operations: evaluate innermost operations first or apply the distributive property.
1 A function is shown:
Problem 1
\( f(x) = 4(3x + 5) \)
What is the value of \( f(12) \)?
Show Work Here:
Final Answer
\( f(12) = \)
2 A function is shown:
Problem 2
\( h(x) = 7(5x + 2) \)
What is the value of \( h(15) \)?
Show Work Here:
Final Answer
\( h(15) = \)
Reflection: Did you calculate the value inside parentheses first, or distribute? Both methods lead to the same result!
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Function Launch Teacher Key
Teacher Answer Key Algebra 1 • Function Notation
Function Evaluation Solutions
Quick Key
#1: 164 | #2: 539
Comprehensive step-by-step breakdown with instructional notes and common misconception alerts.
Reference / Benchmark Problem: \( g(x) = 6(2x + 7) \), find \( g(20) \)
\( g(20) = 6(2(20) + 7) = 6(40 + 7) = 6(47) = \mathbf{282} \)
1 \( f(x) = 4(3x + 5) \) — Find \( f(12) \)
f(12) = 164
Method 1: Order of Operations (Standard)
\( f(12) = 4(3(\mathbf{12}) + 5) \)
\( f(12) = 4(36 + 5) \)
\( f(12) = 4(41) \)
\( f(12) = 164 \)
Method 2: Distributive Property
\( f(x) = 12x + 20 \)
\( f(12) = 12(\mathbf{12}) + 20 \)
\( f(12) = 144 + 20 \)
\( f(12) = 164 \)
Watch out: Students often add \( 3 + 5 = 8 \) before multiplying by 12. Emphasize \( 3 \times 12 \) occurs first inside parentheses.
2 \( h(x) = 7(5x + 2) \) — Find \( h(15) \)
h(15) = 539
Method 1: Order of Operations (Standard)
\( h(15) = 7(5(\mathbf{15}) + 2) \)
\( h(15) = 7(75 + 2) \)
\( h(15) = 7(77) \)
\( h(15) = 539 \)
Method 2: Distributive Property
\( h(x) = 35x + 14 \)
\( h(15) = 35(\mathbf{15}) + 14 \)
\( h(15) = 525 + 14 \)
\( h(15) = 539 \)
Watch out: Multi-digit multiplication error on \( 7 \times 77 \). Encourage mental split: \( (7 \times 70) + (7 \times 7) = 490 + 49 = 539 \).
2-Minute Whole-Class Debrief Prompts:
- "Who substituted first versus who distributed first? Why did one method feel easier with larger numbers?"
- "Why is \( f(12) \) not the same as \( f \times 12 \)?" (Reinforce that \( f \) is the name of the function rule, not a variable).