function below provide the following: a. x- intercepts b. y-intercepts c. end behavior of the graph d. graph of this function f(x)=(x+1)(x-7)(x-1) submit graph.Need correct answer

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nathanshields | High School Teacher | (Level 1) Associate Educator

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a. X-intercepts are roots.  If the function equals 0, that means that one of the three factors is zero.  The values that would make one of the factors zero are:

x = -1, 1, 7

b. The y-intercept occurs when x=0 (that's where the y-axis is, right?).  Setting x = 0, we have f(0) = (1)(-7)(-1) = 7.

y-int = 7

c. End behavior happens when x is very big or very negative: think about this: f(big) = (big+1)(big-7)(big-1).  This is basically the product of three big numbers, which is a big number itself!

But what about when x is very negative?  f(neg) = (neg+1)(neg-7)(neg-1).  This is just the product of three big negative numbers, which is a big negative number itself (neg*neg*neg=neg).

So end behavior is:

`lim_(x->infty) f(x)=infty`


d. Graph by plotting the above info, and you have