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Answer:
A table that has (0,0), (-1,1), (-4, 2) and undefined for any positive x value
Step-by-step explanation:
Reflecting across the y axis just changes the x values, it makes them negative. so has points (0,0), (1,1), (4, 2) and so on. reflecting over the y axis makes them(0,0), (-1,1), (-4, 2) and again so on.
Also good to mention in negative x values are undefined, so flipped over the y axis positive x values are undefined.
As for the answer it doesn't look like any of those shown. The first one is close, but the x values would need to swap their signs.
Function transformation involves changing the form of a function
- The transformation from f(x) to g(x) is a horizontal shift 3 units left, followed by a vertical stretch by a factor of 4
- The x and y intercepts are -0.67 and 1.91, respectively.
- The behavior of g(x) is that, g(x) approaches infinity, as x approaches infinity.
The functions are given as:
<u>(a) The transformation from f(x) to g(x)</u>
First, f(x) is shifted left by 1 unit.
The rule of this transformation is:
So, we have:
Next. f'(x) is vertically stretched by a factor of 4.
The rule of this transformation is:
So, we have:
Hence, the transformation from f(x) to g(x) is a horizontal shift 3 units left, followed by a vertical stretch by a factor of 4
<u>(b) Sketch of g(x)</u>
See attachment
<u>(c) Asymptotes</u>
The graphs of g(x) have no asymptote
<u>(d) The intercepts, and the behavior of f(x)</u>
The graph crosses the x-axis at x =-0.67, and it crosses the y-axis at y = 1.91
Hence, the x and y intercepts are -0.67 and 1.91, respectively.
The behavior of g(x) is that, g(x) approaches infinity, as x approaches infinity.
We know this because, the value of the function increases as x increases
Read more about function transformations at:
