Algebra 2 Problems of the Day (Algebra 2/Trigonometry Regents, January 2012)

Now that I'm caught up with the current New York State Regents exams, I'm revisiting some older ones.

More Regents problems.

Algebra 2/Trigonometry Regents, January 2012

Part I: Each correct answer will receive 2 credits.


25. Which function is one-to-one?

1) f(x) = |x|
2) f(x) = 2^x
3) f(x) = x^2
4) f(x) = sin x

Answer: 2) f(x) = 2^x

In a function, every x has exactly one y. In a one-to-one function, every y also has only one x.

The inverses to an absolute-value, quadratic or sine function will not be functions. The outputs have multiple inputs.

26. If p varies inversely as q, and p = 10 when q = 3/2, what is the value of p when q = 3/5?

1) 25
2) 15
3) 9
4) 4

Answer: 1) 25

If p varies inversely as q then p₁q₁ = p₂q₂

(10)(3/2) = p₂(3/5)

p₂ = (10)(3/2)(5/3) = 25

27.Which equation is graphed in the diagram below?

1) y = 3 cos(π/30 x) + 8
2) y = 3 cos(π/15 x) + 5
3) y = -3 cos(π/30 x) + 8
4) y = -3 cos(π/15 x) + 5

Answer: 4) y = -3 cos(π/15 x) + 5

The minimum for the graph is 2 and the maximum is 8, so the midline is 5. So the equation will end with "+ 5". Eliminate Choices (1) and (3).

The value for Cos(0) is 1, which is the maximum for y = cos x. The graph starts at a minimum, which means that the function starts with -3 not 3. Choice (4) is the solution.

Additionally, the period of a cosine graph is 2π. This graph has a period of 30 (not 30π), and 2π/30 = π/15, which would have eliminated Choices (1) and (3).

End of Part I.

More to come. Comments and questions welcome.

More Regents problems.

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