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Paul [167]
3 years ago
6

PLEASE HELP!! DUE TODAY!! ! 25 POINTS!! Given f (x) = x^4 - 5x^3 - 20x^2 + 60x + 144. Explain how to find the x and y-intercept

and end behavior without graphing technology. Also, explain how to find the x & y-intercept and end behavior with graphing technology
Mathematics
1 answer:
Marta_Voda [28]3 years ago
5 0

the end behavior is that it goes positive and both ends  (we look at x^4 ) and put in -inf and + inf and get +inf both times)

to get the y intercept let x=0  y intercept =144

to find the x intercepts we factor  and find the zeros

using graphing technology  we plot the function

we look at the ends  of the graph if it goes down it goes to - inf, if it goes up it goes to + inf

the y intercept is where x=0

there x intercepts are where it crosses the x axis on the plot (there should be 4 unless some are imaginary)

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Step-by-step explanation:

<u><em>Step(i):-</em></u>

From the graph, the points are R(-4,5), S(1,3),T(-2,-2)

First, the points are reflected over the x-axis then  transform in to

(x,y)→(x,-y)

R(-4,5)→R¹(-4,-5)

S(1,3)→S¹(1,-3)

T(-2,-2)→T¹(-2,2)

<u><em>Step(ii):-</em></u>

Next, The points are shifted to 3 units left then the transform

(x,y)→ (x -3 ,y)

R¹(-4,-5)→ R¹(-4-3, -5) → R¹(-7, -5)

S¹(1,-3)   →   S¹(1-3, -3) →  S¹(-2, -3)

T¹(-2,2)  →   T¹(-2-3, 2)→ T¹(-5, 2)

<u><em>Step(iii):-</em></u>

Now again the points are shifted to '2' units up then transform to

(x,y) )→ (x  ,y+2)

R¹(-7, -5+2) →  R¹(-7, -3)

 S¹(-2, -3+2) →  S¹(-2, -1)

 T¹(-5, 2+2)  →  T¹(-5, 4)

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y - y1 = m(x - x1)

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idu

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