Question

Need ANSWER ASAP

Consider the following transformed function
y = −2 Sin [2( − 45°)] + 1

a) Graph the five key points of Parent function on the provided grid.

b) State the following for the transformed function
Amplitude=
period=
Horizontal Phase shift =
Equation of axis=

c) Graph at least two cycles of the transformed function by transforming the key points of the parent function. (Don’t forget to label the x-axis and y -axis)

Answer 1

See explanation below.

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.