Math / Trigonometry

Question19. Given the function below, find the 5 points amplitude. (The same function will be used for problems 19-22). $y=2 \sin \left(4 x-\frac{\pi}{4}\right)+5$ A. Amp. $=5$ B. Amp. $=4$ C. Amp. $=2$ D. Amp. $=\frac{\pi}{4}$ $A$ B C D

Studdy Solution

STEP 1

1. The function given is in the form $y = A \sin(Bx - C) + D$ .
2. The amplitude of a sine function is determined by the coefficient $A$ in front of the sine term.

STEP 2

1. Identify the coefficient of the sine function.
2. Determine the amplitude from the coefficient.

STEP 3

Identify the coefficient of the sine function in the given equation:
The function is given as $y = 2 \sin \left(4x - \frac{\pi}{4}\right) + 5$ .
The coefficient $A$ in front of the sine function is $2$ .

STEP 4

Determine the amplitude from the coefficient:
The amplitude of a sine function $y = A \sin(Bx - C) + D$ is the absolute value of the coefficient $A$ .
Therefore, the amplitude is:
$\text{Amplitude} = |2| = 2$
The amplitude of the function is $\boxed{2}$ .

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