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Andreas93 [3]
3 years ago
10

Write the equation for the function of the graph below​

Mathematics
1 answer:
riadik2000 [5.3K]3 years ago
6 0

Answer:  (1) y= \sqrt{x+2}-2   (2) y = (x - 3)³

                    D: x ≥ -2  [-2, ∞)      D: -∞ < x < ∞ (-∞, ∞)

                    R: y ≥ -2  [-2, ∞)      R: -∞ < y < ∞ (-∞, ∞)

                    Inc: x > 2 (2, ∞)      Inc: (-∞, 3) ∪ (3, ∞)

                    Dec: never             Dec: never

<u>Step-by-step explanation:</u>

NOTES:

Domain is the x-values.

Range is the y-values.

From left to right: increasing when going up and decreasing when going down. <em>The anchor and turning point are not considered to be increasing or decreasing.</em>

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Read 2 more answers
Let alpha and beta be conjugate complex numbers such that frac{\alpha}{\beta^2} is a real number and alpha - \beta| = 2 \sqrt{3}
miskamm [114]

Answer:

-3+i\sqrt{3} , 1+\sqrt{3}

Step-by-step explanation:

Given that alpha and beta be conjugate complex numbers

such that frac{\alpha}{\beta^2} is a real number and alpha - \beta| = 2 \sqrt{3}.

Let

\alpha = x+iy\\\beta = x-iy

since they are conjugates

\alpha-\beta = x+iy-(x-iy)\\= 2iy= 2i\sqrt{3} \\y =\sqrt{3}

\frac{\alpha}{\beta^2} }\\=\frac{x+i\sqrt{3} }{(x-i\sqrt{3})^2} \\=\frac{x+i\sqrt{3}}{x^2-3-2i\sqrt{3}} \\=\frac{x+i\sqrt{3}((x^2-3+2i\sqrt{3}) }{(x^2-3-2i\sqrt{3)}(x^2-3-2i\sqrt{3})}

Imaginary part of the above =0

i.e. \sqrt{3} (x^2-3)+2x\sqrt{3} =0\\x^2+2x-3=0\\(x+3)(x-1) =0\\x=-3,1

So the value of alpha = -3+i\sqrt{3} , 1+\sqrt{3}

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