Class prep · TJ Algebra 2 Honors
A complete Algebra 2 Honors course, from functions and systems through quadratics, polynomials, logarithms, sequences, conics, trigonometry and probability. Connect equations, graphs and models, then solve original problems and check your reasoning. Every problem has a full worked solution. Built by Neil Kothari, a TJ alumnus.
$395 covers the full school year. The first lesson is free.
Try one. This is a test-level question from the course.
What is the real domain of ?
Answer
, since and .
Full solution
The square root requires , giving .
The denominator separately excludes one, even though the square root is defined there.
Intersect the two conditions. Negative two is included because its numerator is zero and denominator is nonzero.
Where students lose points
Combine domain conditions with and, rather than choosing just one restriction.
Free lesson
Read a function as an input-output assignment and track exactly which inputs and outputs belong.
Start with function notation, domain and range, then connect an equation to its graph and meaning.
True or False: The relation is not a function because the output occurs twice. Justify.
Answer
False. Each input has exactly one output. Different inputs may share an output; the domain is and range is .
Full solution
Inspect each first coordinate, since it is the input. The three distinct inputs each occur with only one output.
The inputs and both lead to four, which is allowed. A function fails only if one input is assigned different outputs.
The range lists distinct attained outputs, so repeated four appears only once in the set notation.
Where students lose points
Do not reverse the definition. A function is single-valued from inputs to outputs; it need not be one-to-one.
What is the real domain of ?
Answer
, because requires .
Full solution
A real square root requires its radicand to be nonnegative, including zero.
Solve . Dividing the equivalent inequality by negative two reverses its direction.
The endpoint is included because its radicand is zero and is defined.
Where students lose points
The domain describes allowable inputs, so solve the radicand condition for , not for the output.
The full lesson and all 13 of its problems, with every worked answer.
How it works
A complete Algebra 2 Honors course for students in grades 9 to 12. Work alongside your school course or study the material in sequence after Algebra 1 and Geometry. Each lesson starts with a concrete example, develops the idea, and shows how to check your reasoning before you try the practice.
What is inside
Who built it
Neil Kothari
TJHSST alumnus · Co-founder, EduAvenues · 10+ years in TJ preparation
Neil is a TJ alumnus and has spent more than a decade working with TJ students and their families. He built this course so students can connect equations and graphs, recognize function families and explain their reasoning. Every problem is written for the course and every answer is checked before it goes in.
Tuition
$395for the full school year
One tuition covers every unit of the course. All 8 units are open now. The Functions, Domain and Range lesson stays free for everyone.