Answer:
B, D, and E.
B: As x approaches negative infinity, g(x) approaches positive infinity.
D: As x approaches positive infinity, g(x) approaches positive infinity.
E: Function g is continuous.
Step-by-step explanation:
To answer this question, we will graph it. Please refer to the graph below.
Let’s go through each of the answer choices.
A) Function g is increasing over the entire domain.
Looking at the graph, we can see that this is not true.
More specifically, the red curve is decreasing over its entire interval.
So, A is not correct.
B) As x approaches negative infinity, g(x) approaches positive infinity.
This is true. As x approaches negative infinity i.e. as we go towards the left of the graph, we can see that our function g(x) (the red curve) is approaching positive infinity.
C) Function g includes an exponential piece and a quadratic piece.
This is false. The first piece is indeed exponential, but the second piece is a cubic, not a quadratic.
D) As x approaches positive infinity, g(x) approaches positive infinity.
Again, this is true. As x approaches positive infinity i.e. As we go towards the right of the graph, we can see that our function g(x) (the blue curve this time) is approaching positive infinity.
E) The function is continuous.
For a function to be continuous, it must have no breaks, jumps, and/or gaps.
We can see that our function does not possess any of the above.
So, g(x) is continuous.
Therefore, the correct statements are B, D, and E.
