Consider the function y = 1/x.
A. What happens to the value of the function as the value of x gets very large?
My answer: the value of the function increases.
B. For what value of x is the function undefined? Explain why.
My answer: 0, because it is not included in the domain.
Please help - I'm not sure about my answers.
A, No
Try experimenting with your calculator
if x = 5000, y = 1/5000 = .0002
if x = 9,000,000, y = 1/9000000 = .000000111..
....
B. yes, x = 0 is not in the domain or else we would have
1/0, which is undefined.
Oh okay, so the value of the function would decrease right?
Because if x = 1, y = 1 but if x = 5, y = 0.20
obviously
A. The value of the function y = 1/x approaches zero as the value of x gets very large. To understand this, let's consider the graph of the function. As x increases, the fraction 1/x becomes smaller and smaller, approaching zero as x goes to infinity. So, the value of the function does not increase, but approaches zero.
So, your original answer that the value of the function increases as x gets very large is not accurate. The correct answer is that the value of the function approaches zero as x gets very large.
B. You are correct that the function is undefined for x = 0. When x is equal to 0, the fraction 1/x results in dividing by zero, which is undefined in mathematics.
To identify the value for which a function is undefined, we need to look for values that would result in a division by zero or any other mathematical operation that is undefined. In this case, when x equals 0, the denominator becomes zero, leading to an undefined result.
Therefore, your answer that the function is undefined for x = 0 is correct.