Graphing functions

 $f\left(x\right)=\ 4\sqrt{x+2}-3$  

Describe the transformation, domain, and range for the provided function. 

• Vertical Stretch by 4, Left 2, Down 3
   $Domain:\ \left[-2,\infty\right)\ \ \ \ \ \ \ \ \ \ \ Range:\ \left[-3,\ \infty\right)$  
  

• Vertical Stretch by 4, Right 2, Up 3 $Domain:\ \left[-2,\infty\right)\ \ \ \ \ \ \ \ \ \ \ Range:\ \left[-3,\ \infty\right)$  

• Vertical Stretch by 4, Left 2, Down 3
   $Domain:\ \left(-\infty,\infty\right)\ \ \ \ \ \ \ \ \ \ \ Range:\ \left(-\infty,\infty\right)$  
  

• Vertical Stretch by 4, Right  2, Up 3 $Domain:\ \left(-\infty,\infty\right)\ \ \ \ \ \ \ \ \ Range:\ \left(-\infty,\infty\right)$  

If f(x) = ∛(x) is reflected over the x-axis, vertically shrunk by a factor of 1/4, and shifted left 9, which equation is correct?

• 1/4 ∛(x + 9)

• 1/4 ∛(x - 9)

• - 1/4 ∛(x + 9)

• - 1/4 ∛(x - 9)

Describe the transformation:

g(x) = f( -x ) -5

• Vertical reflection, move up 5

• Horizontal reflection, move down 5

• Vertical reflection, move down 5

• Horizontal reflection, move up 5

Describe the transformation.

• Left 1 unit, Reflect over x-axis, Up 2 units

• Left 1 unit, Reflect over y-axis, Down 2 units

• Right 1 unit, Reflect over x-axis, Up 2 units

• Right 1 unit, Reflect over y-axis, Up 2 units

• reflect across y=0

• translate left 6 units

• translate right 6 units

• translate up 6 units

• translate down 6 units

The simplest form of a ​ (a)   is called a ​ (b)   . For an exponential function, the parent growth function is ​ (c)   and the parent ​decay function is ​ (d)   . Moving a parent function on a graph is called a ​ (e)   .

• function
• parent function
• transformation

What are the transformations from the parent function?

 $g\left(x\right)=3\sqrt{-x}$  

• Vertical stretch by 3, reflection in x-axis

• Horizontal stretch by 3, reflection in x-axis

• Horizontal shrink by 1/3, reflection in y-axis

• Vertical stretch by 3, reflection in y-axis

Describe the transformation of the following equation:
y=  $\sqrt{x}$  -10

• Right 10 units horizontally

• Up 10 units vertically

• Down 10 units vertically

• Left 10 units horizontally

Identify ALL transformations of f(x)=(1/2)^x+4-3. On your paper explain how your determined that answer.

• Vertical Shift 3 units down.

• Horizontal Shift 4 units left and Vertical Shift 3 units down.

• Horizontal Shift 3 units left and Vertical Shift 4 units left.

• Horizontal Shift 4 units right and Vertical Shift 3 units down.

Which equation has a vertical stretch of 4 and moves up 3?