Help with functions and graphs?

Question

There are a couple questions on my summer pre cal packet regarding functions and graphs that I do not completely understand. I would appreciate if someone could help me understand how to do these problems. For example, how do you determine the shape of the graph when there is no graph? 

 

Directions: Identify the shape of the graph, any transformations (including shifts and reflections). Be sure to indicate the number of units and the direction.

 

*Note: I attempted the first two; would like to know if I'm correct or not.

 

1) h(x) = -|x + 3| 

 

Shape of graph: (I'm assuming it's a parabola)

Reflection: Over the X - Axis

Horizontal Shift: Left 3

Vertical Shift: None

Stretch/Shrink: None

 

2) f(x) = (x-4)² + 11

 

Shape of Graph: 

Reflection: None

Horizontal Shift: Right 3

Vertical Shift: Up 11

Stretch/Shrink: None

 

3) h(x) = √x - 5

 

Shape of graph: _____

Reflection: ____

Horizontal Shift: ____

Vertical Shift: ____

Stretch/Shrink: ____

 

4) f(x) = -³√x-7  -4

 

Shape of graph: ___

Reflection: ___

Horizontal: ___

Vertical: ____

Stretch/Shrink: ____

 

Thank you! 

Answer 1

(1). Shape is an inverted "V", not a parabola.

 

(3). Shape:  same as y = √x

      Reflection:  NONE

      Horizontal shift:  Shift the graph of y = √x five units downward

      Vertical shift:  NONE

      Stretch/shrink:  NONE

 

(4).  Shape:  same as inverted graph of y = ³√x

       Reflection:  in x-axis

       Horizontal shift:  7 units to the right

       Vertical shift:  4 units downward

       Stretch/shrink:  NONE