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1. What is an equation of the graph of y = x 3 y equals , x cubed  under a vertical stretch by the factor 2 followed by a horizontal translation 3 units to the left and then a vertical translation 4 units down?

Problem 2 Finding Zeros of a Transformed Cubic Function

Multiple Choice If a, h, and k are real numbers and a ≠ 0 , eh not equal to 0 comma  how many distinct real zeros does y = − a ( x − h ) 3 + k y equals . negative eh open x minus h close cubed . plus k  have?

1. 0
2. 1
3. 2
4. 3

− a ( x − h ) 3 + k = 0 x  is a zero means it is an  x -intercept, so  y = 0. − a ( x − h ) 3 = − k Subtract  k  from each side . ( x − h ) 3 = k a Divide each side by − a . x − h = k a 3 Take the cube root of each side . x = k a 3 + h Solve for  x . table with 5 rows and 3 columns , row1 column 1 , negative eh . open , x minus h , close cubed . plus k , column 2 equals 0 , column 3 x . isazeromeansitisan . x . minusinterceptcommaso . y equals 0. , row2 column 1 , negative eh . open , x minus h , close cubed , column 2 equals negative k , column 3 cap subtract . k . fromeachside . . , row3 column 1 , open , x minus h , close cubed , column 2 equals , k over eh , column 3 cap divideeachsideby . minus eh . , row4 column 1 , x minus h , column 2 equals , cube root of k over eh end root , , column 3 cap takethecuberootofeachside . . , row5 column 1 , x , column 2 equals , cube root of k over eh end root , , plus h , column 3 cap solvefor . x . , end table

Disregarding multiplicities, the function has a single real zero. The correct answer is B.

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2. What are all the real zeros of the function y = 3 ( x − 1 ) 3 + 6 ? y equals 3 . open x minus 1 close cubed . plus 6 question mark