SOLUTION: 25. State the various transformations applied to the base function ƒ(x) = |x| to obtain a graph of the function g(x) = −|x| + 2. 1. A reflection about the y-axis and a

Algebra.Com
Question 1086373: 25.
State the various transformations applied to the base function ƒ(x) = |x| to obtain a graph of the function g(x) = −|x| + 2.

1. A reflection about the y-axis and a vertical shift upward of 2 units.

2. A reflection about the x-axis and a vertical shift upward of 2 units.

3. A reflection about the y-axis and a vertical shift downward of 2 units.

4. A reflection about the x-axis and a vertical shift downward of 2 units.



Found 2 solutions by stanbon, AnlytcPhil:
Answer by stanbon(75887)   (Show Source): You can put this solution on YOUR website!
State the various transformations applied to the base function ƒ(x) = |x| to obtain a graph of the function g(x) = −|x| + 2.
Answer::
1. A reflection about the y-axis and a vertical shift upward of 2 units.
Cheers,
Stan H.
------------

Answer by AnlytcPhil(1806)   (Show Source): You can put this solution on YOUR website!

First lets get the proper path to start with |x| and end up with
-|x|+2

Step 1.  |x|      <--an upward v-shaped graph with vertex (0,0) going through
                     (1,1) and (-1,1)  
                      
Step 2. -|x|      <--multiply by -1, which reflects the graph
                     across the x-axis. 

Step 3. -|x| + 2  <--add +2, which shifts the graph upward 2 units.

(Always do addition to the right side or subtraction from the right
side last.)

Here they are:

Step 1. f(x) = |x|      <--an upward v-shaped graph with vertex (0,0) going through
                     (1,0) and (-1,0). That's the red graph below:  




                      
Step 2. h(x) = -|x|     <--multiply right side by -1, which reflects the graph
                        across the y-axis.  That's the green graph below:  



Step 3. g(x) = -|x| + 2  <--add +2, which shifts the graph upward 2 units. That's
                  the black graph below.



Edwin
RELATED QUESTIONS

Describe the transformations applied to the graph of y=x^2 to obtain the function f(x) =... (answered by Boreal)
13. State the various transformations applied to the base function ƒ(x) = x2 to obtain a (answered by Boreal)
a new function g(x) is obtained from a given function f(x), where g(x) = 2-f(x). If one... (answered by stanbon)
26. State the various transformations applied to the base function to obtain a graph of (answered by stanbon)
Hi Can I have some help with this function? A function f is given, and the indicated... (answered by stanbon)
Write a function rule g(x) for the given transformations applied to the graph of f(x)=x^2 (answered by josgarithmetic)
Can someone assist me??please. i)state the transformations applied to the graph of... (answered by stanbon)
Identify the transformations of the function ƒ(x) = log_2(2(x + 6)) from the base graph... (answered by lwsshak3)
Identify the transformations of the function ƒ(x) = log22(x + 6) from the base graph g(x) (answered by stanbon)