The functions below could have created this graph will be f(x) = (1/2)x⁴ + x³ + x. Then the correct option is D.
What is the graph of the function?
The collection of all coordinates in the planar of the format [x, f(x)] that make up a variable function's graph.
The graph of the function is given below.
We know that if the degree of the function is odd, then the terminating point of the curve will be a different side.
And if the degree of the function is even, then the function will look like parabola that means both terminating end will be on same side.
Let check all the options.
A. f(x) = x³ + x + 2, the degree of the function is odd.
So, it is incorrect.
B. f(x) = x⁵ + 2x⁴ + 3x, the degree of the function is odd.
So, it is incorrect.
C. f(x) = –x⁴ + 1, the degree of the function is even, but the graph open downward.
So, it is incorrect.
D. f(x) = (1/2)x⁴ + x³ + x, the degree of the function is even and the graph open upward.
So, it is correct.
Then the correct option is D.
More about the graph of the function link is given below.
https://brainly.com/question/9834848
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