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Which of the following graphs represents a function that is strictly increasing?

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Question: Which of the following graphs represents a function that is strictly increasing?

Options:

  1. A graph that slopes downward from left to right.
  2. A graph that slopes upward from left to right.
  3. A horizontal line.
  4. A graph that has both increasing and decreasing intervals.

Correct Answer: A graph that slopes upward from left to right.

Solution: 

A strictly increasing function is one where, for any two points x1 and x2, if x1 < x2, then f(x1) < f(x2), which is represented by a graph that slopes upward from left to right.

Which of the following graphs represents a function that is strictly increasing?

Practice Questions

Q1
Which of the following graphs represents a function that is strictly increasing?
  1. A graph that slopes downward from left to right.
  2. A graph that slopes upward from left to right.
  3. A horizontal line.
  4. A graph that has both increasing and decreasing intervals.

Questions & Step-by-Step Solutions

Which of the following graphs represents a function that is strictly increasing?
  • Step 1: Understand what a function is. A function takes an input (x) and gives an output (f(x)).
  • Step 2: Know what 'strictly increasing' means. A function is strictly increasing if, when you pick two points on the x-axis (let's call them x1 and x2), if x1 is less than x2, then the output for x1 (f(x1)) is less than the output for x2 (f(x2)).
  • Step 3: Look at the graphs provided. You need to find a graph that goes up as you move from left to right.
  • Step 4: Identify the graph that slopes upward. This means that as you move along the x-axis from left to right, the y-values (outputs) should be getting higher.
  • Step 5: Confirm that there are no flat sections or downward slopes in the graph you selected. If the graph only goes up, it is strictly increasing.
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