Which statements are true about function g?
2 answers:
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 <em>x</em> approaches negative infinity, g(x) approaches positive infinity.
This is true. As x approaches negative infinity i.e. as we go towards the <em>left</em> 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 <em>right</em> 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.
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