Question: Which of the following functions has a vertical asymptote?
Options:
f(x) = x^2 + 1
f(x) = 1/(x - 2)
f(x) = e^x
f(x) = log(x)
Correct Answer: f(x) = 1/(x - 2)
Solution:
The function f(x) = 1/(x - 2) has a vertical asymptote at x = 2, where the function is undefined.
Which of the following functions has a vertical asymptote?
Practice Questions
Q1
Which of the following functions has a vertical asymptote?
f(x) = x^2 + 1
f(x) = 1/(x - 2)
f(x) = e^x
f(x) = log(x)
Questions & Step-by-Step Solutions
Which of the following functions has a vertical asymptote?
Step 1: Understand what a vertical asymptote is. A vertical asymptote occurs when a function approaches infinity as the input (x) approaches a certain value.
Step 2: Look at the function f(x) = 1/(x - 2). This function is a fraction where the denominator is (x - 2).
Step 3: Identify when the denominator equals zero. Set (x - 2) = 0 to find the value of x that makes the function undefined.
Step 4: Solve for x. Adding 2 to both sides gives x = 2.
Step 5: Conclude that at x = 2, the function f(x) is undefined, which means there is a vertical asymptote at this point.
No concepts available.
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