Without multiplying, tell which product is larger and why. 5 × 1 3 or 5 × 2 3
2 answers:
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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
and
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.