Determine the range, domain and asymptotes

[JohnRobbo]

i am struggling with these two questions would appreciate any help

q1
f(x) =[FONT=arial, sans-serif]√5x-20[/FONT]

[FONT=arial, sans-serif]i think the range is you add numbers into position of x so you would get so x would have to be greater than 5. so would the answer be x = greater than 5 for the range?

i dont know how to find domain and asymtote.

q2
f(x) = 2 / 6-3x

the range x= greater or equal to 1

dont know how to find domain and asymtote[/FONT][FONT=arial, sans-serif][/FONT]

 

[ksdhart2]

I'd begin by reviewing your book/class notes for the definitions of the three terms "domain," "range," and "asymptote." Currently, you've got the definitions of range and domain backwards. Given a function, the domain is the set of inputs that function can have. You're given two functions of (what variable), so the domain of each function is the set of all values (what variable) can have. Conversely, the range is set of all outputs of the function. I'd also note that your problem statements are ambiguous. For instance, is the first problem:

\(\displaystyle \sqrt{5}x-20\) or \(\displaystyle \sqrt{5x}-20\) or \(\displaystyle \sqrt{5x-20}\)?

The first expression was generated based on exactly what you wrote. Similarly for the second problem, is it:

\(\displaystyle \frac{2}{6}-3x\) or \(\displaystyle \frac{2}{6-3x}\)?

Again, the former is exactly what you wrote. Grouping symbols are important.

In any case, what do you know about square roots? What happens if you take the square root of a negative number? Can the result of a square root ever be negative? What do you know about fractions? What happens if you try to divide by zero?

 

[JohnRobbo]

I'd begin by reviewing your book/class notes for the definitions of the three terms "domain," "range," and "asymptote." Currently, you've got the definitions of range and domain backwards. Given a function, the domain is the set of inputs that function can have. You're given two functions of (what variable), so the domain of each function is the set of all values (what variable) can have. Conversely, the range is set of all outputs of the function. I'd also note that your problem statements are ambiguous. For instance, is the first problem:

\(\displaystyle \sqrt{5}x-20\) or \(\displaystyle \sqrt{5x}-20\) or \(\displaystyle \sqrt{5x-20}\)?

The first expression was generated based on exactly what you wrote. Similarly for the second problem, is it:

\(\displaystyle \frac{2}{6}-3x\) or \(\displaystyle \frac{2}{6-3x}\)?

Again, the former is exactly what you wrote. Grouping symbols are important.

In any case, what do you know about square roots? What happens if you take the square root of a negative number? Can the result of a square root ever be negative? What do you know about fractions? What happens if you try to divide by zero?

q1 is \(\displaystyle \sqrt{5x-20}\)

q2 is\(\displaystyle \frac{2}{6-3x}\)

sorry not very good at putting fractions on forum, my notes arent the greatest for this part of test would appreciate any pointers

 

[Ishuda]

q1 is \(\displaystyle \sqrt{5x-20}\)

q2 is\(\displaystyle \frac{2}{6-3x}\)

sorry not very good at putting fractions on forum, my notes arent the greatest for this part of test would appreciate any pointers

You seemed to have picked up the LaTex for math expressions. Don't know if you have seen it but I generally keep
ftp://ftp.ams.org/pub/tex/doc/amsmath/short-math-guide.pdf
hanging around in a tab on the browser.

You need to review what domain, range, and asymptotes are. A simple (but not complete) explanation is the domain is the values x can take on, the range is the values y can take on as in y=y(x), and asymptotes are either finite values for y where x becomes very large [horizontal asymptote] or where y goes to \(\displaystyle \pm\infty\) for finite x, e.g where a denominator becomes zero, [vertical asymptotes]
For q1: The square root is of 5x-20. What is the 'rule' for square roots?
For q2: Where is the denominator zero? What values can x take on? What values does y [the given expression] take on? What is the behavior of y for large values of x [both positive and negative]?

 

[stapel]

\(\displaystyle \mbox{Q1. }\, f(x)\, =\, \sqrt{\strut 5x\, -\, 20\,}\)

Domain: Can you have negatives inside square roots? So the argument of the square root has to be "greater than or equal to zero", right? What inequality does this give you? What solution do you get?

Range: What values do you get out? You know the endpoint of the graph (the x-value where the domain starts, together with the corresponding y-value), and you know what radical graphs look like. What then (from the picture and the endpoint) is the minimum y-value? What is the maximum y-value? (For one of those questions, the answer is "there isn't one".) So what is the range of y-values?

Asymptote: How is your book defining asymptotes for radicals? (This isn't standard, so we'll need whatever they gave you to use.)

\(\displaystyle \mbox{Q2. }\, f(x)\, =\, \dfrac{2}{6\, -\, 3x}\)

the range x= greater or equal to 1

How did you get this? Did you not notice how this does not match the graph you did?

dont know how to find domain and asymtote

Asymptote: To learn how to find asymptotes, try here.

Domain and range: To learn how to find domains (easy) and ranges (hard), try here.

Once you've learned the basic terms and techniques (which they were supposed to have covered in class before assigning homework), please attempt the exercises. If you get stuck, please reply showing your efforts so far. Thank you!