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How Do We Identify Key Features of Functions from Their Graphs?

Understanding the key features of functions from their graphs can be really fun! Here’s a simple way to break it down:

  1. Intercepts:

    • X-intercept: This is where the graph touches the xx-axis. To find it, set y=0y=0.
    • Y-intercept: This is where the graph touches the yy-axis. To find it, set x=0x=0.
  2. Shape and Slope:

    • Look for parts of the graph that are going up or down. If the graph goes up from left to right, it's increasing. If it goes down, it's decreasing.
    • The steepness, or slope, shows how quickly it rises or falls.
  3. Maxima and Minima:

    • These points show where the graph is at its highest or lowest. You can find them at the peaks (highest points) and the valleys (lowest points) of the graph.
  4. Domain and Range:

    • The domain is all the xx values that the function can have. It represents how far left and right the graph goes.
    • The range is all the yy values. It shows how high and low the graph goes.

By looking at these features, you can really understand what a function does just by checking out its graph!

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How Do We Identify Key Features of Functions from Their Graphs?

Understanding the key features of functions from their graphs can be really fun! Here’s a simple way to break it down:

  1. Intercepts:

    • X-intercept: This is where the graph touches the xx-axis. To find it, set y=0y=0.
    • Y-intercept: This is where the graph touches the yy-axis. To find it, set x=0x=0.
  2. Shape and Slope:

    • Look for parts of the graph that are going up or down. If the graph goes up from left to right, it's increasing. If it goes down, it's decreasing.
    • The steepness, or slope, shows how quickly it rises or falls.
  3. Maxima and Minima:

    • These points show where the graph is at its highest or lowest. You can find them at the peaks (highest points) and the valleys (lowest points) of the graph.
  4. Domain and Range:

    • The domain is all the xx values that the function can have. It represents how far left and right the graph goes.
    • The range is all the yy values. It shows how high and low the graph goes.

By looking at these features, you can really understand what a function does just by checking out its graph!

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