Answered

IDNLearn.com is designed to help you find reliable answers quickly and easily. Get step-by-step guidance for all your technical questions from our dedicated community members.

Which of the following represent [tex]$y$[/tex] as a function of [tex]$x$[/tex]?

Select all that apply.

A. [tex]y = x^2[/tex]
B. [tex]y = x[/tex]
C. [tex]\{(0,5), (1,6), (1,9)\}[/tex]

Sagot :

GinnyAnsweridn
To determine whether each given relation represents [tex]\( y \)[/tex] as a function of [tex]\( x \)[/tex], we need to ensure that each input [tex]\( x \)[/tex] corresponds to exactly one output [tex]\( y \)[/tex]. Let's examine each option step by step:

1. Option [tex]\( y = x^2 \)[/tex]:

- This equation describes a parabola.
- For any given value of [tex]\( x \)[/tex], squaring it yields exactly one value of [tex]\( y \)[/tex].
- For example, if [tex]\( x = 2 \)[/tex], then [tex]\( y = 2^2 = 4 \)[/tex]. Similarly, if [tex]\( x = -2 \)[/tex], then [tex]\( y = (-2)^2 = 4 \)[/tex].
- Every input [tex]\( x \)[/tex] has a unique output [tex]\( y \)[/tex].

Therefore, [tex]\( y = x^2 \)[/tex] represents [tex]\( y \)[/tex] as a function of [tex]\( x \)[/tex].

2. Option [tex]\( y = x \)[/tex]:

- This equation describes a straight line with a slope of 1.
- For any given value of [tex]\( x \)[/tex], the value of [tex]\( y \)[/tex] is exactly the same as [tex]\( x \)[/tex].
- For example, if [tex]\( x = 3 \)[/tex], then [tex]\( y = 3 \)[/tex]. Similarly, if [tex]\( x = -3 \)[/tex], then [tex]\( y = -3 \)[/tex].
- Every input [tex]\( x \)[/tex] has a unique output [tex]\( y \)[/tex].

Therefore, [tex]\( y = x \)[/tex] represents [tex]\( y \)[/tex] as a function of [tex]\( x \)[/tex].

3. Option [tex]\( \{(0,5),(1,6),(1,9)\} \)[/tex]:

- This is a set of ordered pairs.
- For a relation to be a function, each [tex]\( x \)[/tex] value must be paired with exactly one [tex]\( y \)[/tex] value.
- In this relation, the input value [tex]\( x = 1 \)[/tex] is associated with two different [tex]\( y \)[/tex] values (6 and 9).
- This means that the input [tex]\( x = 1 \)[/tex] does not have a unique [tex]\( y \)[/tex] value.

Therefore, [tex]\( \{(0,5),(1,6),(1,9)\} \)[/tex] does not represent [tex]\( y \)[/tex] as a function of [tex]\( x \)[/tex].

In conclusion, the relations [tex]\( y = x^2 \)[/tex] and [tex]\( y = x \)[/tex] represent [tex]\( y \)[/tex] as a function of [tex]\( x \)[/tex], while the set [tex]\( \{(0,5),(1,6),(1,9)\} \)[/tex] does not.
Thank you for joining our conversation. Don't hesitate to return anytime to find answers to your questions. Let's continue sharing knowledge and experiences! Trust IDNLearn.com for all your queries. We appreciate your visit and hope to assist you again soon.