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hjlf
3 years ago
5

"A function is graphed on a coordinate grid. As the domain values approach infinity, the range values approach infinity. As the

domain values approach negative infinity, the range values approach infinity. To which family of functions might the described function belong?
a.reciprocal
b.square root
c.exponential
d.quadratic"

Mathematics
1 answer:
mash [69]3 years ago
4 0
The answer is D. Quadratic. You can think by eliminating those which are wrong. You look at the horizontal line for the domain values and at vertical line for <span>range values.</span>

1. For square root the domain values is always positive (>=0) so it cannot approach to infinity.
2. For exponential as the domain values approach <span>negative infinity, the range values approach to 0 not infinity.
3. For reciprocal as you approach to 0 the range values approach infinty. 

So the only left answer is D. Quadratic.</span>
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A function assigns the values. The function f = xy²-2x² satisfies a conservative vector field F = ∇f.

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

A function assigns the value of each element of one set to the other specific element of another set.

Given F(x,y) = (y² - 4x) i + 2xy j, and it is needed to be known that,

f_x(x,y)=y^2-4x\\f_y(x,y) = 2xy

Let's look for a primitive of y²-4x with regard to x. Because we regard y (and y²) as constants, a primitive of y² is xy², just as a primitive of k is xk (because we treat y² as a constant). Because a primitive of x equals x²/2, a primitive of 4x is 2x². As a result, a primitive of y²-4x is xy²-2x². We can get any other primitive by adding constants, but because we considered y as a constant, we have that.

f(x,y) = xy²-2x²+c(y)

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To learn more about c(y), we shall deduce the formula in terms of y.

2xy=f_y(x,y)

      =\dfrac{d}{dy}(xy^2-2x^2+c(y))\\\\=2xy-0+\dfrac{d}{dy}c(y)\\\\=2xy+\dfrac{d}{dy}c(y)

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3 0
2 years ago
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Answer:

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(x^{2} +10x+25)(x-2)

2) Rewrite x^{2} +10x+25 in the form a^{2} +2ab+b^{2}, where a = x and b = 5.

(x^{2} +2(x)(5)+5^{2} )(x-2)

3) Use Square of Sum: (a+b)^{2} =a^{2} +2ab+b^{2}.

(x+5)^{2} (x-2)

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Half of 4 is 2 . 0.325 is small number.
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