Need help creating a function with asymptotes and other properties

[nathalie27]

Help me make a function for calculus class with certain rules?

I’m also supposed to graph it. The function has to have the following properties:

x-intercepts (−3,0),(2.5, 0), (5,0)

Function Values: (2/3,4), (4,3)

Vertical asymptote x= 1 with behavior lim?(?)=∞ limf(x) =-∞
x→1- x→1+

Horizontal Asymptotes: Y=-2

Discontinuities at ?=1,?=−1,?=4

Limits: lim ?(?)=1, lim ?(?)=2,
?→4 ?→-1+
and lim ?(?)=-1
?→-1-

I’m so scared i don’t even know how to start. Please help!

 

[mmm4444bot]

Hello. In case you've skipped reading the posting guidelines, a summary link appears below. Please explain which parts of the exercise you find confusing. When you say that (2/3,4) and (4,3) are "function values", do you understand those are ordered pairs (i.e., some of those numbers are inputs and the others are outputs)? Have you practiced working with Rational functions before? If so, then what parts do you remember? Do you have experience finding intercepts, asymptotes, limits? Please share your thoughts about this exercise. Thank you!

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[topsquark]

Help me make a function for calculus class with certain rules?

I’m also supposed to graph it. The function has to have the following properties:

x-intercepts (−3,0),(2.5, 0), (5,0)

Function Values: (2/3,4), (4,3)

Vertical asymptote x= 1 with behavior lim?(?)=∞ limf(x) =-∞
x→1- x→1+

Horizontal Asymptotes: Y=-2

Discontinuities at ?=1,?=−1,?=4

Limits: lim ?(?)=1, lim ?(?)=2,
?→4 ?→-1+
and lim ?(?)=-1
?→-1-

I’m so scared i don’t even know how to start. Please help!

Look up some functions with these features and give it a try.

Is this all one question or are there a bunch of different ones thrown together? Creating something that does this is possible but extremely complicated. Take it one step at a time: Start with how you can write a function with the x-intercepts. Then add in the function values. Then the asymptotes, etc.

-Dan

 

[Steven G]

Take it slow.
Step 1:
Plot these 5 points:
x-intercepts (−3,0),(2.5, 0), (5,0)
Function Values: (2/3,4), (4,3)

Step 2:
Draw the following:
Vertical asymptote at x= 1
When x→1^- you have lim?(?)=∞
When x→1⁺ you have lim f(x) =-∞

Step 3:
Using the points you have from steps 1 and 2 and the additional information below draw a graph.
Horizontal Asymptotes: y=-2
and Discontinuities at ?=1,?=−1,?=4

Post back what you got for each step and we'll go from there.

 

[Dr.Peterson]

Help me make a function for calculus class with certain rules?

I’m also supposed to graph it. The function has to have the following properties:

x-intercepts (−3,0),(2.5, 0), (5,0)

Function Values: (2/3,4), (4,3)

Vertical asymptote x= 1 with behavior lim?(?)=∞ limf(x) =-∞
x→1- x→1+

Horizontal Asymptotes: Y=-2

Discontinuities at ?=1,?=−1,?=4

Limits: lim ?(?)=1, lim ?(?)=2,
?→4 ?→-1+
and lim ?(?)=-1
?→-1-

I’m so scared i don’t even know how to start. Please help!

I'd like to see the exact wording of the problem, ideally as an image of the original.

You may be making it harder than it is intended to be; I think @Steven G has the right idea. Our first impression when you say "make a function" is to write the equation of a function, but it probably doesn't say that. You aren't also supposed to graph it; you are only supposed to graph it.

I say that because as requirements pile up, it gets harder and harder to make an equation, even if you knew a lot more than you do; and it looks increasingly like it would be a piecewise function anyway. So don't give any thought to what kind of function it is (e.g. rational function).

Do just as @Steven G said, just making a graph, bit by bit. But when you come to the discontinuities, don't draw them until you've shown the limits there:

Discontinuities at ?=1,?=−1,?=4

Limits: lim ?(?)=1, lim ?(?)=2,
............?→4.............?→-1+
and lim ?(?)=-1
.......?→-1-