Each of 7 students reported the number of movies they saw in the past year. Here is what they reported. 16, 13, 19, 16, 8, 10, 1
2 answers:
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In this we know all three zeros and one point from which the graph pass.
So we will let specific cubic polynomial function of the form
As we know zeros are that point where we will get value of function equal to zero. So it is basically in form
SO in given question zeros are (2 , 0) , (3, 0) and (5,0)
So we can say
So required equation is
![= a[(x^2 - 2x - 3x + 6)(x-5)]](https://tex.z-dn.net/?f=%3D%20a%5B%28x%5E2%20-%202x%20-%203x%20%2B%206%29%28x-5%29%5D)
![= a[(x^2 - 5x+6)(x-5)]](https://tex.z-dn.net/?f=%3D%20a%5B%28x%5E2%20-%205x%2B6%29%28x-5%29%5D)
Now we have one point (0 , -5) from which graph passes.
So we say at x = 0 , f(x) = -5
So required equation of cubic polynomial is
For finding y - intercept we simply plugin x = 0 in given equation.
As we know at x = 0 , value of function is -5.
So y - intercept is -5.
So we will let specific cubic polynomial function of the form
As we know zeros are that point where we will get value of function equal to zero. So it is basically in form
SO in given question zeros are (2 , 0) , (3, 0) and (5,0)
So we can say
So required equation is
Now we have one point (0 , -5) from which graph passes.
So we say at x = 0 , f(x) = -5
So required equation of cubic polynomial is
For finding y - intercept we simply plugin x = 0 in given equation.
As we know at x = 0 , value of function is -5.
So y - intercept is -5.
<h2>Hello!</h2>
The answer is:
The domain of the function is all the real numbers except the number 13:
Domain: (-∞,13)∪(13,∞)
<h2>Why?</h2>This is a composite function problem. To solve it, we need to remember how to composite a function. Composing a function consists of evaluating a function into another function.
Composite function is equal to:
So, the given functions are:
Then, composing the functions, we have:
Therefore, we must remember that the domain are all those possible inputs where the function can exists, most of the functions can exists along the real numbers with no rectrictions, however, for this case, there is a restriction that must be applied to the resultant composite function.
If we evaluate "x" equal to 13, the denominator will tend to 0, and create an indetermination since there is no result in the real numbers for a real number divided by 0.
So, the domain of the function is all the real numbers except the number 13:
Domain: (-∞,13)∪(13,∞)
Have a nice day!