Is the relation a function? y = x2 + 12x + 31
2 answers:
Answer: Yes , is a function.
Step-by-step explanation:
- A relation is said to be a function if each input value (or x-value) corresponds to one unique output value (y-value).
The given relation :
where , and it a polynomial function .
Also, when we draw the graph of the given function [see the attachment ], we can see that each value of x corresponds to exactly one unique y-value.
It means it follows the definition of a function.
Thus , the answer is : Yes , is a function.
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Answer:
x ∈ {2π/3, π, 4π/3} ≈ {2.09440, 3.14159, 4.18879}
Step-by-step explanation:
The equation can be put into standard form by adding 1:
2cos²(x) +3cos(x) +1 = 0
(2cos(x) +1)(cos(x) +1) = 0
Values of cos(x) that make this true* are ...
cos(x) = -1/2 . . . . . . . . . true for x=2π/3, x=4π/3
cos(x) = -1 . . . . . . . . . . . true for x=π
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A graphing calculator can be helpful here, too.
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* from your knowledge of the short table of trig functions and their signs in different quadrants
