LEARN · EXPLAIN · REVISE

Find the x-intercept.

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

高一必修第一册(A版).pdf · 4.4 · PDF 137 / printed page 130

Revisit first: Logarithms

TOPIC 01

Logarithmic functions

Build understanding of logarithmic 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

y=\log_2(x-3)

Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1

Use logarithmic monotonicity after enforcing a positive argument.

Hint 2

A logarithm is zero exactly when its argument is one.

Worked solution

Use logarithmic monotonicity after enforcing a positive argument.
Calculate or simplify this relation.
$0=\log_2(x-3)\Rightarrow x-3=1\Rightarrow x=4$
The intercept must lie inside the domain.

The requested value is 4.

Checks and common pitfalls: The intercept must lie inside the domain.

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

Teacher preparation and assessment

Interpret and use logarithmic functions with domain checks.
Domain and inverse: Logarithmic input is positive; output ranges over the reals.
Monotonicity: The base decides whether comparisons preserve or reverse order.
Close with: conditions → representation → reasoning → check.

Expected reasoning: Logarithmic input is positive; output ranges over the reals.
Expected reasoning: The base decides whether comparisons preserve or reverse order.
Expected correction: Never forget argument positivity when solving inequalities.