Question

Write a cubic binomial whose end behavior is -∞ on the left and ∞ on the right, which is shifted down 5 units and has a vertical stretch factor of 8.

Answer 1

lets take (x + 1)^3

now if we subtract 5 its shifted down 5 units and what do you need to do for a vertical stretch of factor 8?

Answer 2

@cwrw238 Do I put an 8 in front of the parenthesis?

Answer 3

yes

Answer 4

And do I subtract 5 inside the parenthesis?

Answer 5

no - outside

Answer 6

because the whole graph moves down 5

Answer 7

okay but then how do I know that the end behaviors are negative infinity and infinity?

Answer 8

well if you enter very high negatives or very high positive values for x you can see that the values of function approach - and + infinity

Answer 9

@cwrw238 So my final answer is 8(x+1)^3 - 5 ?

Answer 10

yes