高考函数基础诊断
专为一轮复习夯实地基设计。用每天5分钟搞清定义域红线与单调性规则，精准排查概念漏洞与丢分诱因，轻松拿稳函数基础分。
Like Duolingo, but for 高考函数基础诊断. Tomo turns the whole topic into a game you play five minutes a day, until it actually sticks.
A short one: 5 levels across 2 sections, about 10 minutes end to end, roughly 2 days at five minutes a day. It moves through 摸排盲区：筑牢核心概念防线 and 小题落地：从解题步骤反思丢分原因. It starts from scratch.
Free forever · No credit card · iPhone & Android
Key ideas in 高考函数基础诊断
- 求函数定义域必须针对未经化简变形的原解析式进行判定
- 约去含有自变量的因式会掩盖分母不能为零的限制，从而私自扩大定义域
- 定义域不同则两个函数不属于同一函数，后续基于化简式的所有性质分析都会出错
- 偶次根式要求被开方数非负（≥ 0），但奇次根号对正负无限制
- 分式分母不能为 0，当它与偶次根号复合在分母时须严格大于 0
- 对数的真数要求严格为正数（> 0），不能包含 0
- 一次函数的单调性完全由斜率 $k$ 的正负决定，$k>0$ 递增，$k<0$ 递减
- 二次函数以对称轴为界，抛物线在对称轴两侧单调性相反
- 指数与对数函数单调性一致：底数 $a > 1$ 时单调递增，$0 < a < 1$ 时单调递减
- 复合函数单调性遵循'同增异减'原则：外层为减函数时，若要整体递增，内层必须递减
- 外层 $y = \log_{0.5} u$ 底数在 $(0, 1)$ 上是减函数，因此需找内层二次函数的递减区间
- 所有单调区间的讨论必须严格限制在函数的定义域内（本题定义域要求真数大于0）
- 单调区间端点若属于无定义点（如分母为0、对数真数非正）或开区间的边界，必须写成开区间
- 当函数在端点处连续且有定义时，单调区间端点开闭皆可（高考阅卷均给分）
- 极值点或导数为0的点如果本身连续且有定义，纳入单调区间闭端点完全合规，不强制要求写开
- 高考评分标准中明确规定，函数的定义域是集合，作答必须写成区间或集合形式
You've tried the other tabs
Thirty open tabs. Four facts you actually kept.
You watched. You nodded. By Sunday it was gone.
One answer, then back to scrolling.
Eight weeks. You meant to finish. You didn't.
Tomo gives 高考函数基础诊断 the Duolingo treatment: levels, streaks, and quick quizzes that test what you just learned. That game loop is what the tabs above never had, so it's the one you actually finish.
Here's what playing it feels like
A real question from this course. Take your best guess.
如果对 f(x) = (x² - 1)/(x - 1) 直接约分得到 f(x) = x + 1，会带来什么问题？
Get it right to open this lesson and 4 more in the app.
How to learn 高考函数基础诊断, step by step
Go in order. 5 short levels across 2 sections, about 10 minutes in all, five minutes a day.
- 1
摸排盲区：筑牢核心概念防线
- 定义域速查：找出题目里的“隐形红线”
- 单调性诊断：避开符号与区间的常见扣分坑
- 2
小题落地：从解题步骤反思丢分原因
- 基础实战：利用单调性解不等式与比大小
2 sections · 3 units · 5 levels. Built to play, not to enroll.
Questions about 高考函数基础诊断
How do I learn 高考函数基础诊断?
Go in order: start with 摸排盲区：筑牢核心概念防线, then 小题落地：从解题步骤反思丢分原因. On Tomo that's 5 short levels, about 10 minutes in all, played five minutes a day. Start free and play the first level in under a minute.
Is there a Duolingo-style app for 高考函数基础诊断?
Yes. Tomo works like Duolingo: short daily lessons, streaks and quick quizzes. 高考函数基础诊断 is one of its free courses, and you can type any other topic to get a course of your own.
Is the 高考函数基础诊断 course free?
Yes. 高考函数基础诊断 is playable on Tomo's free plan, which doesn't expire. No credit card, no waitlist. Download the app and start your first lesson.
How long does it take to learn 高考函数基础诊断?
5 levels across 2 sections, about 10 minutes of play in total. It's built for five minutes a day, so you finish it a little at a time instead of all at once.
Do I need any background to start 高考函数基础诊断?
No. It's pitched at a beginner level, so it starts where you are and builds up. If you can tap a phone, you can start.
Tomo is in ChatGPT
Tomo is also a ChatGPT plugin: the same playable courses, built and played inside your chat.
Add Tomo to ChatGPT- What to ask
- “Make me a Tomo course on black holes.” “Turn this chat into a Tomo course.”
- What you get
- Quick questions with instant feedback, hearts and stars, ready to play in about a minute.
- Where it goes
- No sign-up to start. Connect your Tomo account and your streak carries on in the app.
You pick the voice
高考函数基础诊断 is taught in the Bestie style: your friend who just gets it. Want a different feel? In the app you can spin up the same topic in any of Tomo's teaching styles. Same facts, totally different vibe.
More Math on Tomo
The Hidden Structure of Fractions
Explore the surprising deeper architecture of rational numbers far beyond elementary arithmetic. Discover how mediants, Farey sequences, continued fractions, and binary trees organize the rationals into a rich geometric system.
Satz des Pythagoras: Kathete und Hypotenuse
Lösen Sie sich von der starren Formel a² + b² = c² und verstehen Sie das fundamentale Prinzip rechtwinkliger Dreiecke. Meistern Sie die präzise Bestimmung von Katheten und Hypotenuse in jeder Lage und bei beliebiger Variablenbeschriftung. Wenden Sie den Satz zielsicher auf komplexe Figuren und reale geometrische Probleme an.
Calculus: Motion, Change, and Proof
Discover how mathematics models a dynamic world through the twin concepts of rate and accumulation. Move from the intuitive mechanics of curves and optimization to rigorous theorems and foundational proofs.
Everyday Arithmetic
Build genuine confidence with the numbers you encounter every day. Master mental math shortcuts, clear-headed multiplication and division, and practical mastery of fractions, decimals, and negative values.
Everyday Mathematical Thinking
Discover how numbers work as a practical tool for everyday clarity rather than a chore of memorization. Learn mental shortcuts for rapid calculation, master back-of-the-envelope estimation, and spot the geometric and probabilistic rules shaping daily choices.
Everyday Market Math
Ditch the phone calculator and shop with total confidence. Learn intuitive mental shortcuts to track cart totals, spot fake deals, calculate discounts, and split bills on the spot.
Start 高考函数基础诊断 today.
Download Tomo, search 高考函数基础诊断, and play your first lesson in under a minute.