Answer:
domain: (4, 1, 0, -1, 1)
range: (2, 3, 0, -1, -3)
Step-by-step explanation:
domain: x-values
range: y-values
I'm answering a bit late, but your answer should be B.) Plot the point (0, -1), move up 2 and right 3, plot the point, and draw the line through these 2 points.
Hopefully this helps!
Answer:
The degree of (f × g × h)(x) is 7.
i.e option a ) 7
Step-by-step explanation:
Given:
![f(x)=(x+9)\\\\g(x)=(x^{2} -4x)\\\\h(x)=(x^{4}+2 x^{3})](https://tex.z-dn.net/?f=f%28x%29%3D%28x%2B9%29%5C%5C%5C%5Cg%28x%29%3D%28x%5E%7B2%7D%20-4x%29%5C%5C%5C%5Ch%28x%29%3D%28x%5E%7B4%7D%2B2%20x%5E%7B3%7D%29)
To Find:
Degree of (f × g × h)(x) = ?
Solution:
For multiplication of given function we require
Law of indices:
![(x^{a} )(x^{b} )=x^{(a+b)}](https://tex.z-dn.net/?f=%28x%5E%7Ba%7D%20%29%28x%5E%7Bb%7D%20%29%3Dx%5E%7B%28a%2Bb%29%7D)
Distributive Property:
(A + B)(C + D) = A (C + D) + B(C +D)
= AC + AD + BC +BD
Now,
![(f\times g\times h)(x) = (x+9)(x^{2} -4x)(x^{4} +2x^{3})\\ \\ =(x(x^{2} -4x) + 9(x^{2} -4x))(x^{4} +2x^{3})\\\\=(x^{3}+5x^{2}-36x)(x^{4} +2x^{3})\\\\=x^{7}+5x^{6}-36x^{5}+2x^{6}+10x^{5}-72x^{4}\\\\=x^{7} +7x^{6}-26x^{5}-72x^{4} \\\\\therefore (f\times g\times h)(x) = x^{7} +7x^{6}-26x^{5}-72x^{4}](https://tex.z-dn.net/?f=%28f%5Ctimes%20g%5Ctimes%20h%29%28x%29%20%3D%20%28x%2B9%29%28x%5E%7B2%7D%20-4x%29%28x%5E%7B4%7D%20%2B2x%5E%7B3%7D%29%5C%5C%20%5C%5C%20%3D%28x%28x%5E%7B2%7D%20-4x%29%20%2B%209%28x%5E%7B2%7D%20-4x%29%29%28x%5E%7B4%7D%20%2B2x%5E%7B3%7D%29%5C%5C%5C%5C%3D%28x%5E%7B3%7D%2B5x%5E%7B2%7D-36x%29%28x%5E%7B4%7D%20%2B2x%5E%7B3%7D%29%5C%5C%5C%5C%3Dx%5E%7B7%7D%2B5x%5E%7B6%7D-36x%5E%7B5%7D%2B2x%5E%7B6%7D%2B10x%5E%7B5%7D-72x%5E%7B4%7D%5C%5C%5C%5C%3Dx%5E%7B7%7D%20%2B7x%5E%7B6%7D-26x%5E%7B5%7D-72x%5E%7B4%7D%20%5C%5C%5C%5C%5Ctherefore%20%28f%5Ctimes%20g%5Ctimes%20h%29%28x%29%20%3D%20x%5E%7B7%7D%20%2B7x%5E%7B6%7D-26x%5E%7B5%7D-72x%5E%7B4%7D)
Degree is highest power raised to the variable.
Therefore here highest power raised to the variable is 7
Therefore degree of (f × g × h)(x) is 7.
Answer:
n = ± 6
Step-by-step explanation:
absolute value equations usually produce 2 solutions
to get the positive solution just solve normally: 2n - 4 = 8
2n = 12
n = 6
to get the negative solution you must take what is in the absolute value bars and multiply by negative one: -(2n) - 4 = 8
-2n - 4 = 8
-2n = 12
n = -6