GED Mathematical Reasoning TestAlgebraic Problem Solving with Graphs and FunctionsMedium
A technician is monitoring the voltage of a circuit. The voltage, V, in volts, over time, t, in milliseconds, is modeled by the function V(t) = 120 * sin(0.5t) + 60. What is the maximum voltage observed in the circuit?
- A180 volts
- B120 volts
- C60 volts
- D240 volts
Show answer & explanationAnswer & explanation
Correct answer: A. 180 volts
The maximum value of sin(x) is 1. Substitute 1 for sin(0.5t) into the function to find the maximum voltage: V_max = 120 * (1) + 60 = 180 volts.
Why the other options are wrong
- B. This is the amplitude, not the maximum voltage.
- C. This is the vertical shift (midline) of the function, not the maximum.
- D. This is twice the amplitude plus the vertical shift, which is incorrect.
Range of Trigonometric Functions (with Transformations)
For a function of the form y = A sin(Bx + C) + D, the amplitude is |A|, and the vertical shift is D. The range is [D - |A|, D + |A|], meaning the maximum value is D + |A| and the minimum is D - |A|.
- Standard sine/cosine range: [-1, 1]
- Amplitude (A) scales the range: [-A, A]
- Vertical shift (D) moves the range: [D-A, D+A]
- Maximum value = D + A
- Minimum value = D - A
Memory trick: Amplitude stretches, Midline shifts – Max is up, Min is down!