What can be said about the function f(x) = |x| at x = 0?
Practice Questions
Q1
What can be said about the function f(x) = |x| at x = 0?
Continuous
Discontinuous
Only left continuous
Only right continuous
Questions & Step-by-Step Solutions
What can be said about the function f(x) = |x| at x = 0?
Step 1: Understand the function f(x) = |x|. This means that for any value of x, f(x) gives the absolute value of x.
Step 2: Find the value of the function at x = 0. Calculate f(0) = |0| = 0.
Step 3: Determine the left limit as x approaches 0. This means looking at values of x that are slightly less than 0. For example, if x = -0.1, then f(-0.1) = |-0.1| = 0.1. As x gets closer to 0 from the left, f(x) approaches 0.
Step 4: Determine the right limit as x approaches 0. This means looking at values of x that are slightly greater than 0. For example, if x = 0.1, then f(0.1) = |0.1| = 0.1. As x gets closer to 0 from the right, f(x) also approaches 0.
Step 5: Compare the left limit and right limit at x = 0. Both limits equal 0.
Step 6: Since the left limit, right limit, and f(0) all equal 0, we conclude that the function f(x) = |x| is continuous at x = 0.
