11th Grade · Week 1 of 36 · Math
Algebra II: function families review; domain/range
1. Hook
- Read (or listen to) what you’re learning. Don’t jump to the quiz.
- Walk the worked example. Then use the interactive lab on this page.
- Guided set → independent set → mastery check → teach-back.
- If you write a paper, stay on campus: Citation Helper, Source Library, Paper Studio.
This is self-paced homeschool on Life Academy. Everything you need is on this page.
Can you take the square root of any number? Divide by any number? Those two questions decide a function's domain.
Then: lab → guided → quiz → teach it back. The lab is the lesson, not a decoration.
2. Teach
Review the parent function families (linear, quadratic, cubic, square root, absolute value, reciprocal, exponential) and find domain and range.
Standards alignment: CCSS.MATH.CONTENT.HSF (domain-level; works with any state’s standards)
STEM this week is Algebra II: function families review; domain/range: units, a model, and a check another student could repeat.
- Domain = all allowed inputs; range = all resulting outputs.
- Restrictions: no square root of a negative (in the reals) and no division by zero.
- Interval notation: [a, b] includes endpoints; (a, b) excludes them; ∞ always gets a parenthesis.
f(x) = √(x − 2) needs x − 2 ≥ 0, so domain [2, ∞) and range [0, ∞). g(x) = 1/(x − 3) has domain all reals except 3, written (−∞, 3) ∪ (3, ∞); its range excludes 0.
Parent shapes: y = x² is a U with range [0, ∞); y = |x| is a V with range [0, ∞); y = 2ˣ has range (0, ∞) and a horizontal asymptote y = 0; y = x³ has domain and range all reals.
- h(x) = √(6 − 2x).
- Need 6 − 2x ≥ 0.
- −2x ≥ −6, so x ≤ 3 (flip the inequality when dividing by a negative).
- Domain (−∞, 3]; range [0, ∞).
State the domain and range of k(x) = 1/(x + 4) and m(x) = √(x + 5) − 1 in interval notation.
Forgetting to flip the inequality when dividing by a negative, or saying every function has domain all reals.
Domain restrictions are real limits: you cannot sell negative items or divide a bill among zero people.
No classroom teacher today — this page is the lesson. Follow the how-to, then the lab, then the quiz. Follow Lesson Studio, then the lab, then the quiz. Open Transcripts for credits and grades.
Interactive lab (on this page)
Change one variable. Record what happened. This model is the lab — not an off-site sim.
Play & explore
Hands-on practice for this lesson. Your progress saves automatically.
Your work — type it here
Type the answer. Then tap Check my work. This is the assignment — not optional reading.
3. Guided practice
Try these with me — type the missing word, then check.
Reveal the thinking
Look for even roots (inside ≥ 0) and denominators (≠ 0); solve those conditions to get the domain.
4. Independent practice
Work the set. Check when finished — this is practice (mastery quiz is next).
5. Mastery check
Scored quiz — results save to your gradebook.
Show the math — don't only tap a letter
The lab is the worked example you can move. Then the quiz checks that you own Algebra II: function families review; domain/range.
Research Desk · Transcripts · Gradebook
Honest limit: We did not film a custom movie for every core lesson. The teach-back, the on-page lab, and the campus library are the curriculum. The teach-back, the on-page lab, and Lesson Studio are the lesson.
6. Reflection / teach-back
Teach-back: Explain Algebra II: function families review; domain/range in your own words. Give one example and name the usual mistake.