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Citrus2011 [14]
3 years ago
5

Can you please help me with these piece wise function things

Mathematics
1 answer:
julsineya [31]3 years ago
8 0
Plug the domain into the function and the y values you get will be [0, 7) and [5,11)
Putting the ranges for each piece together, the lowest number in the range is 0 and the highest number is 11. The zero is included since the inequality sign was ansl equal to. The 11 is not included since it was not equal to.
[0,11) is the range.
Letter A
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The sum of three consecutive integers is 21 larger than twice the smallest integer. find the integers.
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Which of the following is an even function g(x) = (x – 1)2 + 1g(x) = 2x2 + 1g(x) = 4x + 2g(x) = 2x
GuDViN [60]
An even function can be reflected about the y axis and map onto itself
example: y=x^2

an odd function can be reflected about the origin and map onto itself
example: y=x^3


a simple test is the following

if f(x) is even then f(-x)=f(x)
if f(x) is odd then f(-x)=-f(x)


so

even function
subsitute -x for each and see if we get the same function
remember to fully expand these

g(x)=(x-1)^2+1=x^2-2x+1+1=x^2-2x+2 is the original one

g(x)=(x-1)^2+1
g(-x)=(-x-1)^2+1
g(-x)=(1)(x+1)^2+1
g(-x)=x^2+2x+1+1
g(-x)=x^2+2x+2
not same because the original has -2x
not even


g(x)=2x^2+1
g(-x)=2(-x)^2+1
g(-x)=2x^2+1
same, it's even

g(x)=4x+2
g(-x)=4(-x)+2
g(-x)=-4x+2
not the same, not even

g(x)=2x
g(-x)=2(-x)
g(-x)=-2x
not same, not even



g(x)=2x²+1 is the even function
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