when it comes to checking if a function is even or odd, it boils down to changing the argument, namely x = -x, and if the <u>resulting function is the same as the original</u>, then is even, if the <u>resulting function is the same as the original but negative</u>, is odd, if neither, well then neither :).
anyway, that said, let's first expand it and then plug in -x,
![\bf f(x)=(x^2-8)^2\implies f(x)=(x^2-8)(x^2-8)\implies f(x)=\stackrel{FOIL}{x^4-16x^2+64}\\\\[-0.35em]~\dotfill\\\\f(-x)=(-x)^4-16(-x)^2+64\qquad \begin{cases}(-x)(-x)(-x)(-x)=x^4\\(-x)(-x)=x^2\end{cases}\\\\\\f(-x)=x^4-16x^2+64\impliedby \stackrel{\textit{same as the original}}{Even}](https://tex.z-dn.net/?f=%20%5Cbf%20f%28x%29%3D%28x%5E2-8%29%5E2%5Cimplies%20f%28x%29%3D%28x%5E2-8%29%28x%5E2-8%29%5Cimplies%20f%28x%29%3D%5Cstackrel%7BFOIL%7D%7Bx%5E4-16x%5E2%2B64%7D%5C%5C%5C%5C%5B-0.35em%5D~%5Cdotfill%5C%5C%5C%5Cf%28-x%29%3D%28-x%29%5E4-16%28-x%29%5E2%2B64%5Cqquad%20%5Cbegin%7Bcases%7D%28-x%29%28-x%29%28-x%29%28-x%29%3Dx%5E4%5C%5C%28-x%29%28-x%29%3Dx%5E2%5Cend%7Bcases%7D%5C%5C%5C%5C%5C%5Cf%28-x%29%3Dx%5E4-16x%5E2%2B64%5Cimpliedby%20%5Cstackrel%7B%5Ctextit%7Bsame%20as%20the%20original%7D%7D%7BEven%7D%20)
Answer:
z = 8
Step-by-step explanation:
PythagoreanTheorem
a^2 + b^2 = c^2
a and b stand for the legs while c stands for the hypotenuse. Since we have the numeral for one of the legs and the hypothenuse, we can plug those into the formula.
a^2 + 15^2 = 17^2
a^2 = 64
a = 8
Answer:
D) g(x) is shifted 4 units to the left and 6 units down
Step-by-step explanation:
When -6 is added to the y-value, it moves the point on the graph down 6 units. Compared to f(x), g(x) is 6 units down.
Transforming the function using f(x -h) shifts its graph h units to the right. Here, we have h=-4, so the graph is shifted 4 units to the left.
Answer:
I do not see that any of your options will work.
Step-by-step explanation:
a) and b) have a false first statement because f(1) = 96, not 12
c) would create the sequence 96, 1152, 13824
d.) would create the sequence 96, 192, 384. 768...
I believe the correct answer would be
f(1) = 96 f(n) = ½f(n-1) n ≥ 2
which could be either c) or d) if taking potential typographic errors into account. Recording a "2" or "12" where a "½" ought to be.
