Math  /  Algebra

QuestionGiven the function y=x3y=x^{3}, what are the parameters of the transformed function y=15(x+2)3+9y=\frac{1}{5}(x+2)^{3}+9 and what is the effect of each parameter on the graph of the original function? a=15a=\frac{1}{5}, vertical stretch about the xx-axis by a factor of 15\frac{1}{5} h=2h=-2, horizontal translation 2 units left k=9k=9, vertical translation 9 units up a=5a=5, vertical stretch about the xx-axis by a factor of 5 h=2h=-2, horizontal translation 2 units left k=9k=9, vertical translation 9 units right a=5a=5, vertical stretch about the xx-axis by a factor of 5 h=2h=-2, horizontal translation 2 units right k=9k=9, vertical translation 9 units down a=15a=\frac{1}{5}, vertical stretch about the xx-axis by a factor of 15\frac{1}{5} h=9h=9, horizontal translation 9 units left k=2k=-2, vertical translation 2 units down

Studdy Solution
Match the identified parameters and effects with the given options:
- a=15 a = \frac{1}{5} , vertical stretch about the x x -axis by a factor of 15\frac{1}{5} - h=2 h = -2 , horizontal translation 2 units left - k=9 k = 9 , vertical translation 9 units up
This matches with the first option provided.
The parameters and their effects are: - a=15 a = \frac{1}{5} , vertical stretch about the x x -axis by a factor of 15\frac{1}{5} - h=2 h = -2 , horizontal translation 2 units left - k=9 k = 9 , vertical translation 9 units up

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