Identify the parent function and describe the transformation(s) (or wrtite "none").

Question

columns:
Parent functions
Reflection
Translation(s)
Rows
13.) y=(x-7)^3
14.) y=x-11
15.) y=sqr(x+5-3)
16.) y=-(x-9)^2
17.) y=-|x+3|-1
18.) y=2^-x +6

Answer 1

Here's the identification of the parent functions and the descriptions of their transformations for each of the provided equations:

| Parent functions | Reflection | Translation(s) | |--------------------------|-----------------------------|---------------------------------------| | 13.) y = (x - 7)³ | None | Right 7 units | | 14.) y = x - 11 | None | Down 11 units | | 15.) y = √(x) | None | Left 5 units, Down 3 units (the corrected form is √(x + 5) - 3) | | 16.) y = x² | Yes (across x-axis) | Right 9 units | | 17.) y = |x| | Yes (across x-axis) | Left 3 units, Down 1 unit | | 18.) y = 2^x | None | Up 6 units |

Notes:

• For 15, the equation provided seems to linguistically imply the square root function, but based on the structure, if you meant √(x + 5) - 3, those would be the transformations.
• The parent function for 17 is the absolute value function |x|; thus, the reflection is across the x-axis.
• Transformations are identified based on shifts in the x and y coordinates from the parent function.