The equation of the given graph for the function g(x) is [tex]f(x) = x^4 - x^2 -2[/tex]. so option D is correct. The graph of f(x) is shifted down by a factor of 2 on the y-axis.
How to shift the graph vertically up or down?
- To shift the graph upwards vertically, add a factor(according to the shift) to the y-coordinate.
- To shift the graph downwards vertically, subtract a factor(according to the shift) from the y-coordinate.
How the given graph is shifted?
The given graph [tex]f(x)=x^4 -x^2[/tex] is shifted downwards on the y-axis.
And named g(x)
The shift in the y-axis is by 2 units
So,
g(x) = f(x) - 2
= [tex]x^4-x^2-2[/tex]
Therefore, the equation of the given graph when shifted is [tex]g(x)=x^4-x^2-2[/tex]
Learn more about transformations on graphs here:
https://brainly.com/question/15162303
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