Question

given the graph of the function ( f(x) ) below, what happens to ( f(x) ) when ( x ) is a small positive number?

a. ( f(x) ) is a very large positive number.
b. ( f(x) ) is a very small positive number.
c. ( f(x) ) is a negative number with a large absolute value.
d. ( f(x) ) is a negative number with a small absolute value.

Explanation:

Step1: Analyze the graph near \(x = 0^{+}\)

When \(x\) is a small positive number (\(x\to0^{+}\)), we look at the behavior of the function \(F(x)\) from the right - hand side of \(x = 0\).

Step2: Determine the trend

As \(x\) approaches \(0\) from the positive side (\(x>0\) and \(x\) is very small), the \(y\) - values (values of \(F(x)\)) of the function go to positive infinity.

Answer:

A. \(F(x)\) is a very large positive number