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Bad White [126]
3 years ago
6

Determine whether each function is even, odd, or neither.

Mathematics
2 answers:
Ray Of Light [21]3 years ago
7 0

Answer:

Please check the explanation.

Step-by-step explanation:

<u>Even Functions:</u>

The function is unchanged when it is reflected about the y-axis.

i.e.

f(-x) = f(x)

<u>Odd Functions:</u>

The function is unchanged when it is rotated 180° about the origin.

i.e.

f(-x) = -f(x)

<u>Neither Functions:</u>

f(-x) ≠ -f(x)

Let us check the given functions:

  • f(x) = Vx²9

plug –x in for x

f(-x) = V(-x)²9

f(-x) = Vx²9

f(-x) = f(x)

Therefore, the function f(x) = Vx²9 is even function.

  • g(x) = |x-3|

plug –x in for x

as

f\left(-x\right)=|x+3|

and

-f\left(x\right)=-\left|x-3\right|

so

f(-x) ≠ f(x)

f(-x) ≠ -f(x)

Thus,

g(x) = |x-3| is neither an even nor an odd function.

  • g(x) = x + x²

plug –x in for x

g(-x) = (-x) + (-x)²

g(-x) = -x + x²

g(-x) = -(x-x²)

so

f(-x) ≠ f(x)

f(-x) ≠ -f(x)

Thus, it is neither an even nor an odd function.

Thus,

g(x) = x + x² is neither an even nor an odd function.

AlekseyPX3 years ago
7 0

Answer:

First is even

Second is neither

Third is odd

Last one is neither

Have a great day

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Answer:

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Step-by-step explanation:

<u>Mathematical Modeling</u>

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This problem requires to build a model for the yearly cost of a small and successful business.

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Using proportions, the selling prices are given as follows:

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2. $15.29.

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4. $20,280.

<h3>What is a proportion?</h3>

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

To find the selling prices, we have to multiply the original prices by either 1.02(2% sales tax) or 1.04(4% sales tax), hence they are given as follows:

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