Limits, Continuity & Differentiability
General
Grade 12
Question:
<p>Functions <span class="math-inline">\(S\to T\)</span>. Which TRUE?</p>
<strong>A</strong>
B
<strong>C</strong>
<strong>D</strong>
Step-by-Step Solution
Key Concept: General
<div class="solution"><p>(A) Infinitely many functions: each of uncountably many points maps to one of 4 values ✓. (B) Strictly increasing from S to T: impossible on each component. (C) Continuous functions: each component maps to single value, 4³=64≤120 ✓. (D) Every continuous function is differentiable: locally constant ⟹ derivative=0 ✓. <strong>Answer: (A),(C),(D)</strong></p><div class="key-concept"><strong>Key Concept:</strong> Continuous functions from open intervals to discrete sets are locally constant</div></div>
Correct Answer: A,C,D