Question

Need ANSWER ASAP

Answer 1

Answer:

See explanation below.

Step-by-step explanation:

Given transformed function:

$y=-2 \sin \left[2(x-45^{\circ})\right]+1$

Part (a)

The parent function of the given function is:  y = sin(x)

The five key points for graphing the parent function are:

• 3 x-intercepts  →  (0°, 0)  (180°, 0)  (360°, 0)
• maximum point  →  (90°, 1)
• minimum point  →  (270°, -1)

(See attachment 1)

Part (b)

Standard form of a sine function:

$\text{f}(x)=\text{A} \sin\left[\text{B}(x+\text{C})\right]+\text{D}$

where:

• A = amplitude (height from the mid-line to the peak)
• 2π/B = period (horizontal distance between consecutive peaks)
• C = phase shift (horizontal shift - positive is to the left)
• D = vertical shift (axis of symmetry: y = D)

Therefore, for the given transformed function:

$y=-2 \sin \left[2(x-45^{\circ})\right]+1$

• Amplitude = -2
• Period = 2π/2 = π
• Phase shift = 45° to the right
• Equation of axis of symmetry:  y = 1

Part (c)

See attachment 2.