Table of contents

0. Review of Algebra4h 18m
1. Equations & Inequalities3h 18m
2. Graphs of Equations43m
3. Functions2h 17m
4. Polynomial Functions1h 44m
5. Rational Functions1h 23m
6. Exponential & Logarithmic Functions2h 28m
7. Systems of Equations & Matrices4h 6m
8. Conic Sections2h 23m
9. Sequences, Series, & Induction1h 22m
10. Combinatorics & Probability1h 45m

3. Functions

Intro to Functions & Their Graphs

College Algebra

3. Functions

Intro to Functions & Their Graphs

Previous problemNext problem

0:50 minutes

Problem 27

Textbook Question

Determine whether each equation defines y as a function of x. y = ±√(x-2)

Verified step by step guidance

Understand the definition of a function: A relation is a function if each input (x-value) corresponds to exactly one output (y-value).

Examine the given equation: \( y = \pm \sqrt{x-2} \).

Recognize that the \( \pm \) symbol indicates two possible values for \( y \) for each \( x \) where \( x \geq 2 \).

Consider the implications: For any \( x \geq 2 \), there are two possible values for \( y \) (one positive and one negative), which means \( y \) is not uniquely determined by \( x \).

Conclude that the equation does not define \( y \) as a function of \( x \) because it violates the definition of a function by providing two outputs for a single input.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above

Video duration:

50s

Play a video:

Was this helpful?

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Function Definition

A function is a relation that assigns exactly one output (y) for each input (x). For an equation to define y as a function of x, every x-value must correspond to a single y-value. If an x-value can produce multiple y-values, the relation is not a function.

Vertical Line Test

The vertical line test is a visual way to determine if a graph represents a function. If any vertical line intersects the graph at more than one point, the relation is not a function. This test helps to quickly assess whether y can be uniquely determined from x.

Square Root Function

The square root function, represented as y = ±√(x-2), indicates that for each x-value greater than or equal to 2, there are two corresponding y-values: one positive and one negative. This duality means that the equation does not define y as a function of x, as it fails the definition of a function.