Which of the functions below could have created this graph?
1 answer:
Answer:
A
Step-by-step explanation:
Two facts need to guide your answer.
One
The highest power is odd: you know this because an even power would start on the left come down do it's squiggles if had any and wind up on the right going up.
This graph comes down on the left does it's squiggles and then goes further down on the right. That's the behavior of something whose highest power is odd.
Two
The leading coefficient, the number in front of the highest power must be minus. If it was positive as in y = x^3 the graph would be the mirror image of what it is.
Argument
B and D cannot be true. The highest power is even.
C is false because the leading coefficient is + 1.
So that leave A which is the answer.
The graph is included with this answer
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1. horizontal shrink by factor of 2/3 means multiply outside the f(x) or outside the x^2 by 2/3:
(2/3)•f(x)
2. translation left 5 units means "x+5" inside:
(2/3) • f(x+5)
3. tranlate down 2 units means "-2" outside:
(2/3) • f(x+5) -2
or (2/3) (x+5)^2 - 2
or