Question
Compare the graph of the function with the graph of f(x) = IxI. Describe the transformation. g(x) = -4Ix – 2I – 1
- Moves to the right by 1 unit, goes up by 4 unit and gets vertically stretched.
- Moves to the right by 2 units, goes down by 1 unit and gets vertically compressed.
- Moves to the right by 2 units, goes down by 1 unit, gets reflected across the x-axis and vertically stretched.
- Moves to the right by 4 units, goes up by 1 unit and gets reflected across the x-axis and vertically compressed.
Hint:
A function is defined as a relation between a set of inputs having one output each. In simple words, a function is a relationship between inputs where each input is related to exactly one output.
The correct answer is: Moves to the right by 2 units, goes down by 1 unit, gets reflected across the x-axis and vertically stretched.
We have the graph of f(x) = |x|. We have to describe the transformations to get the graph of g(x) = -4I(x – 2)I – 1.
Comparing the above equation with f(x) = a I(x – h)I + k, we get h = 2.
So, graph moves to the right by 2 units.
Also, k = -1.
So, graph moves down by 1 unit.
And, a = -4.
So, graph gets reflected across the x-axis and gets vertically stretched.
Hence, the correct option is C.
A function is generally denoted by f(x) where x is the input. The general representation of a function is y = f(x).
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