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.
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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
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