write an equation for a function that has vertical asymptotes at x=3 & x=-10

Answer:

[tex] \frac{5}{ {x}^{2} + 7x - 30} [/tex]

Step-by-step explanation:

We can write a rational function.

We need to make sure our denominator both have zeroes at 3 and 10.

Set an equation equal to zero to find the function

[tex]0 - x = 3[/tex]

[tex]0 - x = - 10[/tex]

[tex]0 - ( - 3) = = 3[/tex]

[tex]0 - 10 = 10[/tex]

So we would represent that's as

[tex]x - 3[/tex]

and

[tex]x + 10[/tex]

Multiply the two binomial together.

[tex](x - 3)(x + 10) = {x}^{2} + 7x - 30[/tex]

Let our numbetator be any interger.

Use any equation as long as the quadratic is the denominator and the interger is the numerator.

[tex] \frac{5}{ {x}^{2} + 7x - 30 } [/tex]

can you help me with this, please? ​

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ODE TO AN OTTER
I ought to be an otter, ‘cause when all is said and done
I could play along the riverbank, or stretch out in the sun.
I’d swim beneath the water, or backstroke up on top.
I’d dive in like a graceful swan, or do a belly flop.
My days would be so peaceful as a furry, swimming mammal
As opposed to bearing burdens like a one-humped desert camel.
I wouldn’t want to herd sheep like a working collie dog
Or end up an amphibian—a turtle, toad, or frog.
But oh, to be an otter! It would be a stroke of luck
Just to spend all day a-swimmin’, or a-rollin’ in the muck.
But oh, as fate would have it, I’m required to spend my time
Doing schoolwork. What a pity. It seems like such a crime.
The month of May has ended, and all across the nation
The schools have shut their doors, and all of the kids are on vacation.
Yet here it’s still the school year, and it can’t end too soon,
But the days are standing still, stretching till the end of June.
Ah, the otter, who, when sunshine makes the heat rise at the shore,
Stays within its coolsome burrow, eating clams and snails and more.
It swims along the river, catching crayfish, frogs, and trout.
I’d be an awesome otter—of that I have no doubt. Right now I watch the summer tapping at each window pane
And count the days till school is out, and I can swim again.
I’ll walk in glorious mud that squeezes coolness through my toes
And skip along the river, free from tests and schoolwork woes.
Till then, I’ll be an otter, but only in my head,
And start the summer early there, along the riverbed.
‘Cause if I was an otter and could romp and roll and roam,
I wouldn’t have to think of what to write for my class poem.



My days would be so peaceful as a furry, swimming mammal / As
opposed to bearing burdens like a one-humped desert camel.

What does the word burdens mean in the sentence above?

A. doubts
B. feelings
C. objects
D. rivers



Yet here it’s still the school year, and it can’t end too soon, / But the
days are standing still, stretching till the end of June.

What does the author mean by the phrase the days are standing still?

F. The days seem to pass by slowly.
G. The days are full of difficult work.
H. The speaker’s school day is longer than at most schools.
I. There are more school days left than the speaker thought.





I’ll walk in glorious mud that squeezes coolness through my toes / And
skip along the river, free from tests and schoolwork woes.

How would the effect of these lines be different if the author had used the word
walk instead of skip?

A. The speaker would seem less carefree.
B. The speaker would seem more friendly.
C. The speaker would seem to miss school.
D. The speaker would seem less serious.



What effect does the author’s use of language such as ‘cause, a-swimmin’, and
awesome create in the poem?

F. It makes the speaker sound casual.
G. It makes the speaker sound persuasive.
H. It makes the speaker seem caring toward all animals.
I. It makes the speaker seem knowledgeable about otters.



The end of the poem is ironic because the speaker.

A. decides to write a poem about an otter.
B. turns into an otter and swims away from school.
C. changes her mind and doesn’t want to be an otter.
D. has finished the poem that seemed too hard to write.

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