LEARN · EXPLAIN · REVISE

Prove that the difference of these two exponentials is odd.

Read the idea, work independently, then explain what changed.

高一必修第一册(A版).pdf · 4.2 · PDF 118 / printed page 111

Revisit first: Exponents

TOPIC 01

Exponential functions

Build understanding of exponential functions through definitions, contrasting cases and justified applications.

Use one hint at a time. A correction explains what changed, not just the final answer.

01 / Standard#Your turn

g(x)=2^x-2^{-x}

Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1

Replace x by −x in both terms.

Hint 2

The two terms exchange positions.

Worked solution

g is odd on R.

Checks and common pitfalls: A difference of non-odd functions can still be odd.

Reasoning checklist · self / teacher assessment

Think first. Reveal a hint when the class is ready.

Teacher preparation and assessment

Interpret and use exponential functions with domain checks.
Base: A real exponential base is positive and different from one.
$y=a^x$
Growth and decay: Bases above one increase; bases between zero and one decrease.
Close with: conditions → representation → reasoning → check.

Expected reasoning: A real exponential base is positive and different from one.
Expected reasoning: Bases above one increase; bases between zero and one decrease.
Expected correction: An exponential never reaches its zero asymptote.