At Westonci.ca, we provide reliable answers to your questions from a community of experts. Start exploring today! Get quick and reliable solutions to your questions from knowledgeable professionals on our comprehensive Q&A platform. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.
Sagot :
To determine which statement is true about the equation
[tex]\[ y = -3x^2 + 4x - 11 \][/tex],
we need to analyze the nature of this equation in terms of relations and functions.
### Understanding Relations and Functions
- Relation: A relation is a set of ordered pairs [tex]\((x, y)\)[/tex]. In simpler terms, it shows how two quantities are related.
- Function: A function is a special type of relation where every input [tex]\( x \)[/tex] is related to exactly one output [tex]\( y \)[/tex].
### Analyzing the Given Equation
The given equation is a quadratic equation in the form
[tex]\[ y = ax^2 + bx + c, \][/tex]
where [tex]\( a = -3 \)[/tex], [tex]\( b = 4 \)[/tex], and [tex]\( c = -11 \)[/tex].
1. Relation:
- This quadratic equation can be expressed as a set of ordered pairs [tex]\((x, y)\)[/tex]. For every value of [tex]\( x \)[/tex] that we substitute into the equation, we get a corresponding value of [tex]\( y \)[/tex]. Therefore, it clearly defines a relation.
2. Function:
- For an equation to be a function, every [tex]\( x \)[/tex] must map to exactly one [tex]\( y \)[/tex].
- A quadratic equation is a polynomial of degree 2, which forms a parabolic curve. Each value of [tex]\( x \)[/tex] corresponds to exactly one value of [tex]\( y \)[/tex]. There are no instances where a single [tex]\( x \)[/tex] value produces multiple [tex]\( y \)[/tex] values in a quadratic equation.
### Conclusion
Given that the equation [tex]\( y = -3x^2 + 4x - 11 \)[/tex] fits both the criteria of a relation and the stricter criteria of a function:
The correct statement is:
A. It represents both a relation and a function.
[tex]\[ y = -3x^2 + 4x - 11 \][/tex],
we need to analyze the nature of this equation in terms of relations and functions.
### Understanding Relations and Functions
- Relation: A relation is a set of ordered pairs [tex]\((x, y)\)[/tex]. In simpler terms, it shows how two quantities are related.
- Function: A function is a special type of relation where every input [tex]\( x \)[/tex] is related to exactly one output [tex]\( y \)[/tex].
### Analyzing the Given Equation
The given equation is a quadratic equation in the form
[tex]\[ y = ax^2 + bx + c, \][/tex]
where [tex]\( a = -3 \)[/tex], [tex]\( b = 4 \)[/tex], and [tex]\( c = -11 \)[/tex].
1. Relation:
- This quadratic equation can be expressed as a set of ordered pairs [tex]\((x, y)\)[/tex]. For every value of [tex]\( x \)[/tex] that we substitute into the equation, we get a corresponding value of [tex]\( y \)[/tex]. Therefore, it clearly defines a relation.
2. Function:
- For an equation to be a function, every [tex]\( x \)[/tex] must map to exactly one [tex]\( y \)[/tex].
- A quadratic equation is a polynomial of degree 2, which forms a parabolic curve. Each value of [tex]\( x \)[/tex] corresponds to exactly one value of [tex]\( y \)[/tex]. There are no instances where a single [tex]\( x \)[/tex] value produces multiple [tex]\( y \)[/tex] values in a quadratic equation.
### Conclusion
Given that the equation [tex]\( y = -3x^2 + 4x - 11 \)[/tex] fits both the criteria of a relation and the stricter criteria of a function:
The correct statement is:
A. It represents both a relation and a function.
We appreciate your visit. Hopefully, the answers you found were beneficial. Don't hesitate to come back for more information. Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. We're dedicated to helping you find the answers you need at Westonci.ca. Don't hesitate to return for more.