A function is graphed on a coordinate grid. As the domain values approach infinity, the range values approach infinity. As the d
omain values negative infinity, the range values approach infinity. To which family of functions might the described functions belong?
A) reciprocal
B) square root
C) exponential
D) quadratic
A) reciprocal
B) square root
C) exponential
D) quadratic
2 answers:
Answer:
D) Quadratic
Step-by-step explanation:
A function is graphed on a coordinate grid.
- As the domain values approach infinity, the range values approach infinity.
Domain: If then
Range:
- As the domain values negative infinity, the range values approach infinity.
Domain: If then
Range:
We need to choose correct option which follows given domain and range.
Only quadratic function will follow the rule because it has even degree polynomial.
Quadratic function:
Degree = 2 and leading coefficient is positive.
Domain:
Range:
Hence, D is correct option.
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Solving for
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Next, check the concavity of the squared distance to verify that a minimum occurs at this value. If the second derivative is positive, then the critical point is the site of a minimum.
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The minimum distance is then
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Next, check the concavity of the squared distance to verify that a minimum occurs at this value. If the second derivative is positive, then the critical point is the site of a minimum.
You have
so indeed, a minimum occurs at
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