Given the graph of the function F(x) below, what happens to F(x) when x is a negative number with a large absolute value?
2 answers:
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Answer:
- The function must be shifted right 1 unit.
- The function must be shifted up 4 units.
- The function must be stretched vertically by a factor of 3.
Step-by-step explanation:
There are some transformations for a function f(x):
If , then the function is shifted up "k" units.
If , then the function is shifted down "k" units.
If , then the function is shifted left "k" units.
If , then the function is shifted right "k" units.
If and
, then the function is stretched vertically by a factor of "b".
If and
, then the function is compressed vertically by a factor of "b".
In this case we have the following parent function :
And the function :
Based on the explained before, we can describe the transformations necessary to transform the graph of to the graph of
:
- The function must be shifted right 1 unit.
- The function must be shifted up 4 units.
- The function must be stretched vertically by a factor of 3.
The required function -
The parent function is translated to the right 2 units.
We have to find which absolute value function has a graph that is wider than the parent function.
The parent function
with the vertex (0,0)
The parent function is translated to the right 2 units.
Transformation to the right,
f(x)→f(x-b) , the graph of f(x) is shifted towards right by b unit.
Same as the graph f(x) is shifted towards the right by 2 units and forms a graph of h(x).
If the graph is wider than the parent function then the function must be in the form of,
Where the value of k must be less than or equal to 1. If k is more than 1 then the graph is compressed.
So, let it be k=1
Therefore, The required absolute value function is,
We plot the graph of both the equations in which translation is shown.
Refer to the attached graph below.
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