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

2. Graphs of Equations

Graphs and Coordinates

College Algebra

2. Graphs of Equations

Graphs and Coordinates

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1:46 minutes

Problem 20

Textbook Question

In Exercises 11–26, determine whether each equation defines y as a function of x. y = - √x +4

Verified step by step guidance

Step 1: Understand the definition of a function. A function is a relation where each input (x-value) has exactly one output (y-value).

Step 2: Analyze the given equation: y = -\sqrt{x} + 4.

Step 3: Consider the domain of the function. The square root function \sqrt{x} is only defined for x \geq 0.

Step 4: For each x-value in the domain, substitute it into the equation to see if it results in a unique y-value.

Step 5: Conclude whether the equation defines y as a function of x by checking if each x-value corresponds to exactly one y-value.

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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). This means that for every value of x in the domain, there is a unique corresponding value of y. To determine if an equation defines y as a function of x, we must check if each x-value leads to one and only one y-value.

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 an equation defines y as a function of x by examining its graphical representation.

Square Root Function

The square root function, represented as y = -√x + 4, involves taking the square root of x, which can yield both positive and negative values. However, since the equation specifies y as a negative square root, it will produce a unique y-value for each non-negative x-value, thus satisfying the definition of a function.