Which of the following statements is true regarding the function f(x) = |x|?
Practice Questions
Q1
Which of the following statements is true regarding the function f(x) = |x|?
Continuous everywhere
Discontinuous at x = 0
Continuous only for x > 0
Discontinuous for x < 0
Questions & Step-by-Step Solutions
Which of the following statements is true regarding the function f(x) = |x|?
Step 1: Understand what the function f(x) = |x| means. The absolute value function takes any number x and makes it positive. For example, |3| = 3 and |-3| = 3.
Step 2: Identify what it means for a function to be continuous. A function is continuous if you can draw it without lifting your pencil. This means there are no breaks, jumps, or holes in the graph.
Step 3: Look at the graph of f(x) = |x|. It forms a 'V' shape that meets at the point (0, 0).
Step 4: Check the point x = 0. The function f(0) = |0| = 0, so the function is defined at this point.
Step 5: Since there are no breaks or jumps in the graph of f(x) = |x|, we conclude that it is continuous everywhere, including at x = 0.
