Vault Of Euclid

Evaluating and Finding the Domain and Range of a Function of Three Variables

Functions and graphs warmup

Let \( f(x, y, z) = \frac{x^2 + z + 3 \sin y}{x + 2y - z} \). Evaluate \( f \) at the point \( (3, 0, 2) \) and find the domain and range of \( f \).

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What you need first

Evaluating algebraic expressions
Identifying the domain of a rational function
Normal vectors of planes in 3D space

What this problem tests

Tests the ability to evaluate multivariable functions, identify domain restrictions (division by zero), and reason about the range of a function.

This is a standard introductory problem in multivariable calculus, familiarizing students with functions of more than two variables.

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