what is the range of the function graphed below

Guri Bee

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20-10-2024

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Understanding the Range of a Function: A Visual Approach

When we talk about the range of a function, we're essentially asking: What are all the possible output values the function can produce? To understand this, we need to look at the graph of the function.

Imagine the function as a machine. You put in an input value (an x-value), and the machine spits out an output value (a y-value). The range is the set of all possible output values the machine can produce.

Visualizing Range on a Graph

The easiest way to determine the range is to look at the graph of the function. Here's how:

1. Identify the y-axis: The range represents the values the function takes on vertically, so focus on the y-axis.

2. Look for the highest and lowest points: Find the highest and lowest points on the graph. These points will give you the maximum and minimum values for the range.

3. Consider any "gaps" or "holes": Does the graph have any gaps or holes? These could indicate values that are not included in the range.

Example:

Let's look at an example to illustrate this. Imagine a function graphed like this:

[Insert a graph of a function here, for example, a parabola opening upwards with a vertex at (0,1)]

• Highest point: The graph goes infinitely upwards. This means there is no maximum value for the range.

• Lowest point: The lowest point on the graph is at (0,1).

• Gaps or holes: There are no gaps or holes in the graph.

Therefore, the range of this function is all real numbers greater than or equal to 1. We can write this in interval notation as [1, ∞).

Real-World Applications:

Understanding the range of a function has practical applications in various fields:

• Engineering: Engineers use range to analyze the limits of a system's output, ensuring safety and efficiency.
• Finance: Financial analysts use range to understand the potential fluctuations of stock prices or other investments.
• Science: Scientists use range to interpret experimental data and identify the limits of their measurements.

Key Takeaways:

• The range of a function is the set of all possible output values.
• You can determine the range visually by looking at the graph of the function.
• Pay attention to the highest and lowest points and any gaps or holes in the graph.

Remember, practice makes perfect! As you work with more functions and graphs, you'll become more comfortable identifying their ranges and understanding their significance.