What would this look like if a write a function g whose graph represents the indicated transformation of the graph of f?

1. f(x)= |x| translation of 5 units left and 2 units up

2. f(x)=x^2; reflection in the c axis and translation 8 units left

#1: |x+5|+2

#2: -(x+8)^2

type that stuff in at wolframalpha.com and you can see the results. #2 is at

http://www.wolframalpha.com/input/?i=plot+plot+x^2%2C-%28x%2B8%29^2+for+-20%3C%3Dx%3C%3D20

To write a function g(x) that represents a transformation of the graph of f(x), you need to understand the effects of each transformation. Let's break down the given transformations for each case:

1. f(x) = |x| translation of 5 units left and 2 units up:
- Translation of 5 units left shifts the graph horizontally to the right by 5 units.
- Translation of 2 units up shifts the graph vertically upwards by 2 units.

To incorporate these transformations into the function g(x), follow these steps:
- Start with the original function f(x) = |x|.
- Apply the translation by changing the input, x, to (x + 5) to shift it 5 units to the left.
- Apply the translation by adding 2 to the whole function to shift it 2 units up.
- Combine these steps to get the function g(x) = |x + 5| + 2.

2. f(x) = x^2; reflection in the c-axis and translation 8 units left:
- Reflection in the c-axis means flipping the graph vertically.
- Translation of 8 units left shifts the graph horizontally to the right by 8 units.

To express these transformations in the function g(x), follow these steps:
- Start with the original function f(x) = x^2.
- Apply the reflection by changing the sign of the function to -x^2.
- Apply the translation by changing the input, x, to (x - 8) to shift it 8 units to the left.
- Combine these steps to get the function g(x) = -x^2 - 8.

These new functions, g(x), correctly represent the indicated transformations of the graphs of f(x).