Question

Help i needa graduate

Answer 1

Answer: A

Explanation:

for a function y = Asin(bx + c), an amplitude equals to |A| (10 in this case), and the period equals to 2π/b (1/2 * π in this case).

Answer 2

`\textsf{A)} \quad \rm amplitude = 10, \; period=(1)/(2)\pi`

Explanation:

The sine function is periodic, meaning it repeats forever.

The general formula for a sine function is:

`\boxed{y = A \sin(B(x + C)) + D}`

where:

• |A| is the amplitude (height from the mid-line to the peak).
• 2π/B is the period (horizontal length of one cycle of the curve).
• C is the phase shift (horizontal shift - positive is to the left).
• D is the vertical shift.

Given function:

`y=-10\sin 4x`

Comparing the given function with the general formula:

• |A| = |-10| = 10
• B = 4
• C = 0
• D = 0

Therefore, the given function has no horizontal or vertical shift.

The amplitude of the function is 10.

The period of the function is:

`\textsf{Period}=(2\pi)/(B)=(2\pi)/(4)=(1)/(2)\pi`