HELP For each equation, state the parent function and list all transformations

Question

For each equation, state the parent function and list all transformations

1. y = 3|𝑥 + 5| − 7
2. y = (-x³)/(2) + 4
3. y = 5 - √(2x)/(3)
4. y = (-4x)² - 3

Answer 1

y = 3|𝑥 + 5| − 7

The parent function is y= |x|.

Transformations: First the graph y=|x| shifts horizontally 5 units to the left, then a vertical stretch by a factor of 3 away from the x axis and finally a vertical shift of 7 units downwards.

y = (-x³)/(2) + 4

The parent function is y=x³

Transformations: The graph of y=x³ is reflected about the y axis and compressed towards the x-axis by a factor of 1/2. Then shifted up by 4 units.

y = 5 - √(2x)/(3)

The parent function is y=√x

Transformations: The graph y=√x is stretched away from the y axis by a factor of 2/3 and reflected about the x axis and finally shifted up by 5 units.

y = (-4x)² - 3

The parent function is y=x²

Transformations: The graph of y=x² is compressed towards the y-axis by a factor of 4 and reflected about the y axis and finally shifted down by 3 units.