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soldier1979 [14.2K]
3 years ago
5

What is the range of the given function?

Mathematics
1 answer:
slava [35]3 years ago
7 0
{y/y=-9,-3,0,5,7} the range are the y values of a function or relation
You might be interested in
Help with these precalculus problems, please.
likoan [24]
Yay, easy peasy, nice refresher


53. evaluate for x=infinity
we get 100/(infiniy^2-5) which is basically 100/infinity which is a very small number so about 0



54.
vertical assemtotes, neato
that is where the denomenator equals 0
but wait, simplify first
ok, fraction is simplified (anything factored out would be a hole)
so set the denom to 0 and solve
x^2-5=0
(x-√5)(x+√5)=0
x=-√5 and √5
vertical assemtotes at x=-√5 and x=√5




55. horizontal assemtotes
for the function p(x)/f(x)

if p(x) has lower degree than f(x) then y=0 is the horizontal assemtote

if p(x) has equal degree to f(x) then divide the leading coefients of p(x) and f(x)

if p(x) has greater degree than f(x) then we got slant assemtotes

100/(x^2-5)
100 has lower degree than x^2
y=0 is the horizontal assemtote



56. evalate for x=-5
we get -150/-10=150/10=15
the limit is 15



57. that negative on the right side means that we must approach it from the left
let's see if we can factor out the denomenator
nope
so go and evaluate values like 4, 4.5, 4.9, etc, approaching x=5 from the left
we keep getting smaller and smaller valuse
this make sense because as x approaches 5, we get 30(c)/(c-5) where c is close to 5, and as c appraoches 5 very close, the top part is appraoching 150 but the bottom approaches a very small negative number, and if we do something like 150/-0.00000000001, we get a very negative number
the limit is negative infinity

alternately, you could figure that there is a vertical assemtote at x=5 so we can see that if we aproximaate closer and closer values, we get smaller values. so from what we know about assemtotes, expecially vertical ones, we say that it approaches negative infinity




58.
evalauating we get infintity/inifinty, not helpful
hmmm, is there a horizontal assemtote to help us?
the degree of top is higher so we got a slant assemtote
the only way is to use long division to divide the top by the bottom (see attachment)
we get
\frac{1}{2}x-\frac{1}{4}+\frac{\frac{1}{4}}{2x+1}
the slant assemtote is y=\frac{1}{2}x-\frac{1}{4}
as you can see, as x approaches infinity, y also will approach infinity











ANSWERS:
53. 0
54. VA is x=-√5 and x=√5
55. HA is y=0
56. the limit is 15
57. the limit is -∞
58. the limit is ∞

6 0
3 years ago
What is the average rate of change in profit from Hour 5 to Hour 10?
snow_lady [41]

Answer:

d

Step-by-step explanation:

so at 5 hours he  was at a profit of 900 and 5 hours later he is at a profit 1500 then you can sub tract 900 from 1500 which gives you 600

8 0
3 years ago
Can someone help me, with this problem, I really need the procedure ​
aleksklad [387]

Answer:

In which standard u are???

Step-by-step explanation:

Of which chapter is it???

3 0
3 years ago
On a bike trip across the United States, Rodney notes that he covers about 190 miles every four days. If he continues at this ra
Feliz [49]
You will have to add 190 with 95 and that will be 285 because he rides 190 miles in FOUR days and you will need to know the half of 190 to get 2 days because each day he would ride 47.5 miles each day and 47.5+47.5=95.

The Answer is 285.
4 0
4 years ago
SHOW YOUR WORK PLEASE! Jim is trying to improve his speed on the track so he can qualify for the State Championships. As he is r
alex41 [277]

Answer:

4 m/s²

Step-by-step explanation:

Acceleration = (106-70)/9

= 36/9

= 4ms^-2

4 0
3 years ago
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