Select the correct answer from each drop-down menu. Use the given functions represented by the equation and the graph to complete the statements.

f(x)=2x^3 - 3x^2 + 5x + 7

As x approaches positive infinity, f(x) approaches [negative infinity, positive infinity, zero] and g(x) approaches [negative infinity, positive infinity, zero]. The y-intercept of function f is [equal to, less than, greater than] the y-intercept of function g.

f(x) approaches positive infinity.

g(x) approaches negative infinity.

the y-intercept of f(x) is less than the y-intercept of g(x).

Step-by-step explanation:

the highest power of x in f(x) is 3, and it has a positive sign. so, the bigger x the more the x³ part will dominate.

therefore, with x going to positive infinity, also f(x) goes to positive infinity.

the graph of g(x) clearly dives down never to come back up or flatten out. so, with x going to positive infinity, g(x) goes to negative infinity.

the y-intercept of f(x) = f(0).

that means the functional value when x=0.

so, for x=0 this means

y = 2×0³ - 3×0² + 5×0 + 7 = 7

the graph of g(x) shows that g(0) is 8.

so f(0) is less than g(0).