Table of contents
- 0. Review of Algebra4h 16m
- 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 19m
- 10. Combinatorics & Probability1h 45m
2. Graphs of Equations
Graphs and Coordinates
5:18 minutes
Problem 45
Textbook Question
Textbook QuestionDetermine whether each relation defines y as a function of x. Give the domain and range. See Example 5. y=√(4x+1)
Verified Solution
This video solution was recommended by our tutors as helpful for the problem above
Video duration:
5mPlay 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 where each input (x-value) corresponds to exactly one output (y-value). To determine if a relation defines y as a function of x, we check if any x-value is paired with more than one y-value. For example, the relation y = √(4x + 1) is a function because for each x, there is only one corresponding y.
Recommended video:
5:57
Graphs of Common Functions
Domain
The domain of a function is the set of all possible input values (x-values) that can be used without causing any mathematical issues, such as division by zero or taking the square root of a negative number. For the function y = √(4x + 1), the domain is determined by the condition 4x + 1 ≥ 0, leading to x ≥ -1/4.
Recommended video:
3:43
Finding the Domain of an Equation
Range
The range of a function is the set of all possible output values (y-values) that result from the domain. For the function y = √(4x + 1), since the square root function only produces non-negative outputs, the range is y ≥ 0. This means that as x varies within the domain, y will always be zero or greater.
Recommended video:
4:22
Domain & Range of Transformed Functions
Watch next
Master Graphs & the Rectangular Coordinate System with a bite sized video explanation from Patrick Ford
Start learningRelated Videos
Related Practice