A trig function given below. Describe the transformations from its parent function. Graph one period of it using 5-point method and write its range. y = 2 sin(x+\pi) + − 1

Question

A trig function given below. Describe the transformations from

its parent function. Graph one period of it using 5-point method and write
its range.
y = 2 sin(x+
`\pi`) + − 1

Answer 1

Parent function: y = sin(x)

Transformations:

1) horizontal translation of pi units towards left

2) stretch parallel to y-axis with factor "2'

3) vertical translations of 1 unit downwards

Range: [-3 , 1]

Explanation:

Parent function: y = sin(x)

Transformations:

1) horizontal translation of pi units towards left

2) stretch parallel to y-axis with factor "2'

3) vertical translations of 1 unit downwards

Sketch the graph using 5 points listed below:

1) (0, -1)

2) (pi/2, -3)

3) (pi, -1)

4) (3pi/2, 1)

5) (2pi, -1)

Range: [-3 , 1]