Answer :
Answer:
f(n) has larger output values as n increases.
Step-by-step explanation:
Priya is comparing two functions: [tex]f(n)=10n^2[/tex] and g(n)=3(2n)
To find out which has greater output values as n gets very large and which has larger output values :
[tex]f(n)=10(n^2)[/tex] and g(n)=3(2n)
Put n=1 we get
[tex]f(1)=10(1)^2[/tex] and g(1)=3[2(1)]
f(1)=10 and g(1)=6
Put n=2 we get
[tex]f(2)=10(2)^2[/tex] and g(2)=3[2(2)]
f(2)=10(4) and g(2)=3.(4)
f(1)=40 and g(1)=12
and so on
Therefore the f(n) has greater output values as n gets large value
Therefore f(n) has larger output values
For any value of n, the function f(n) will give larger output than g(n).
What is a Function?
A function assigns the value of each element of one set to the other specific element of another set.
In order to know which function will give greater output. we will substitute 2, 1, 0, -1, and -2. Therefore,
1. When n=2
[tex]f(n)=10n^2\\f(2)=40\\\\g(n)=3\cdot 2n\\g(2)=12[/tex]
2. When n=1
[tex]f(n)=10n^2\\f(1)=10\\\\g(n)=3\cdot 2n\\g(1)=6[/tex]
3. When n=0,
[tex]f(n)=10n^2\\f(0)=0\\\\g(n)=3\cdot 2n\\g(0)=0[/tex]
4. When n=-1
[tex]f(n)=10n^2\\f(-1)=10\\\\g(n)=3\cdot 2n\\g(-1)=-6[/tex]
5. When n=-2
[tex]f(n)=10n^2\\f(-2)=40\\\\g(n)=3\cdot 2n\\g(-2)=-12[/tex]
As we can see that for any value of n, the function f(n) will give larger output than g(n).
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