The graph that represents the functions f(x) = θx^4 and g(x) = 2√x is a bit difficult to determine without knowing the value of θ, but we can make some general observations.
The function f(x) = θx^4 is a polynomial function, which means it will have a smooth, continuous curve with no breaks or jumps. Also, since the highest power of x is 4, we know that the function will be relatively flat near the origin and become steeper as x increases or decreases.
On the other hand, the function g(x) = 2√x is a radical function, which means it will have a curve that is initially flat near the origin and then gradually becomes steeper as x increases. Since g(x) involves a square root, the graph of g(x) will only be defined for x ≥ 0.
Based on these observations, we can conclude that the graph that represents f(x) = θx^4 is likely to be a smooth, continuous curve that is relatively flat near the origin and becomes steeper as x increases or decreases, while the graph that represents g(x) = 2√x is likely to be a curve that is initially flat near the origin and then gradually becomes steeper as x increases.
Therefore, without knowing the specific value of θ, it is difficult to identify the graph that represents the functions f(x) = θx^4 and g(x) = 2√x with certainty.