Which of the following statements about the graph of a function is true if it is

Practice Questions

Q1
Which of the following statements about the graph of a function is true if it is continuous everywhere?
  1. It has no breaks or holes.
  2. It must be a polynomial function.
  3. It can only be a linear function.
  4. It must have at least one x-intercept.

Questions & Step-by-Step Solutions

Which of the following statements about the graph of a function is true if it is continuous everywhere?
  • Step 1: Understand what a function is. A function is a relationship where each input has exactly one output.
  • Step 2: Learn about graphs. A graph is a visual representation of a function, showing how inputs relate to outputs.
  • Step 3: Know what 'continuous' means. A continuous function means you can draw its graph without lifting your pencil.
  • Step 4: Identify what breaks or holes in a graph are. Breaks or holes occur when there are jumps or missing points in the graph.
  • Step 5: Conclude that if a function is continuous everywhere, it means there are no breaks or holes in its graph.
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