## sparrow2 one year ago if x is a variable then does it have infinite number of values?

1. anonymous

Depends on the context, for mathematics then mainly yes, for real world/physics applications there are limits.

2. anonymous

this is the question im assigned: Does the domain change uner the following transformation of y-log x? Explain. (vert stretch by 5 and horiz. stretch by 2)

3. anonymous

*under

4. anonymous

**and its y=log x . sorry

5. anonymous

domain changes from the horizontal stretch, increases the x values that maps to y values

6. anonymous

by stretch by 2 im guessing you mean expand and not divide by 2

7. anonymous

yeah its expanding horizontally by a factor of 2

8. anonymous

oh wait sorry as a log graph it won't change the domain

9. anonymous

THANK YOU <3

10. Study_together

It depends but I still think its values are infinite. Please click on the best response if you like the post.

11. anonymous

what if its limited to an equation with limited solutions etc.

12. anonymous

then it becomes limited

13. ganeshie8

Define $$x$$ as the variable that represents solution to the quadratic equation $\large x^2-2x+1=0$ how many values does $$x$$ have ?

14. anonymous

Factorised into (X-1)^2=0, 1 solution

15. sparrow2

x=1 is solution and it is "uknown"

16. SolomonZelman

if x is a variable then does it have infinite number of values? YES, I would say. And here are some examples of why I say this. -------------------------------------------- Take any logarithmic function: $$\large\color{black}{ \displaystyle y=\log(x+a)+c }$$ (with any side shift a AND any vertical shift c) Note: The domain is not impacted by C (and nor is the range since it goes infinitely up and down). Now, the log is only defined in this case, if $$\large\color{black}{ \displaystyle x+a>0 }$$, and thus: $$\large\color{black}{ \displaystyle x>-a }$$, and knowing that no restriction on how large (x+a) can get your domain is: (-a, +∞) So if x is over the interval (-a, +∞), then (regardless of the value of a), x takes on infinite number of values. -------------------------------------------- Obviously, any polynomial is known to be continuous over interval (-∞,+∞). This way for any polynomial function $$\large f(x)$$, you get that the domain of y=f(x) is (-∞,+∞) So, here again x takes on infinite number of values. -------------------------------------------- Consider any function!! and you will either get that the domain is (-∞, +∞) OR (s, +∞) OR (-∞, s) (where s is some number)

17. SolomonZelman

So unless you are taking about a function that has a restriction of a≥x≥b, or some sort of limitation fron x to go infinitely to the left or right, (then) x takes on an infinite number of values.

18. SolomonZelman

Usually though, if you are taking a limit of the function, such that: $$\large\color{slate}{\displaystyle\lim_{x \rightarrow ~a}f(x)}$$ $$\Huge\color{blue}($$ or, $$\large\color{slate}{\displaystyle\lim_{x \rightarrow ~a^+}f(x)}$$ or, $$\large\color{slate}{\displaystyle\lim_{x \rightarrow ~a^-}f(x)}$$ $$\Huge\color{blue})$$ then, it would have a value, unless you're going into an undefined direction like: $$\large\color{slate}{\displaystyle\lim_{x \rightarrow ~0^+}\log_{a}(x)}$$ $$\large\color{slate}{\displaystyle\lim_{x \rightarrow ~a}\frac{c}{x-a}}$$ (for left-sided, right-sided or two sides limit DNE) $$\large\color{slate}{\displaystyle\lim_{x \rightarrow ~\infty}ax^{b}}$$ (for b>0) (or other examples where you meet asymptotes or just an infinite growth of x)

19. SolomonZelman

igtg

20. anonymous

I was just answering the first main question, unless a variable is defined as being part of a function only then it would be infinite, but if it is an unknown in an equation when it can be solved for then it is limited to the value of those solutions.

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