0.05 kilogramos.................
First step is to simplify the equation into a form that we are familiar with graphing, in this case the simplest way i believe is to factorise the denominator. There are many methods of factorising quadratics but in this case my preferred method would be as follows:
x^2-3x-10, because it is a quadratic equation we know it can be factorised into the form (x+a)(x+b), we know that -10 is the product of a and b, therefore a and b can only be +/-1 and -/+10, or +/-5 and -/+2, the next step is to see which of these factors sum to equal -3, in this case it will be +2 and -5, therefore x^2-3x-10 can be factorised into (x+2)(x-5).
We have now simplified the function into f(x)= (x+2)/(x+2)(x-5), we can still simplify the function further though:
(x+2)/(x+2)(x-5), the numerator and denominator have a common factor therefore we can divide the numerator and the denominator by that factor, ((x+2)/(x+2))/((x+2)(x-5)/(x+2))= 1/(x-5)
The function is now in it's simplest form, so we will now graph it. As a side note you can't perfectly "graph" any function by hand so instead we will sketch the function, to sketch a function you need to know the general shape of the function and any x/y intercepts or asymptotes.
Functions of the form a/(bx+c) are reciprocal functions, you need to be able to remember what reciprocal function looks like to be a able to sketch them by hand, they look something like this https://www.desmos.com/calculator/df2wiewhsz. To work out the x-intercept we will assign f(x) as 0, 0=1/(x-5), multiply both sides by (x-5), (x-5)0=1, 0=1, 0 doesn't equal 1 therefore there is no x-intercept but instead there is an asymptote at y=0. To work out the y-intercept we will assign x as 0, f(x)=1/(x-5), f(x)=1/-5, therefore the only y-intercept is at coordinates (0.-0.2). All reciprocal functions have 2 asymptotes, we have already found one of them, by making f(x)=0, to find the other asymptote we will make 1/(x-5)=∞, 1/0=∞, therefore x-5 has to equal 0, therefore the second asymptote will be x=5.
after putting all of this together the graph should look something like this https://www.desmos.com/calculator/bibeeu7xtv
Answers:
Domain = [-3, 3]
Range = [-1, 2]
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Explanation:
The domain is the set of all allowed x inputs. Visually, the left-most point is when x = -3, so -3 is the smallest allowed x input. We have a closed circle at this endpoint, so this endpoint x value is included. In contrast, if you had an open circle, then you would exclude the endpoint.
Similarly, we have a closed endpoint at the other side as well when x = 3. This is the largest allowed x value. The domain is the set of x values such that 
meaning x is between -3 and 3, including both endpoints. This translates to the interval notation of [-3, 3]. The square brackets say "include the endpoint".
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The range is the set of possible y outputs of a function. The lowest the function goes is when y = -1, and the highest is when y = 2. We include both endpoints. The range as a compound inequality is 
which converts to the interval notation of [-1, 2]
Step-by-step explanation:
but it's given = -4
which is incorrect
Again , 8^2 = 64
but it's given = √64
so option C and D are not true
