Domain and range from graphs
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The document discusses domain and range for different types of functions. It provides examples of the domain and range for a parabola, square root function, and cubic function. The domain is the set of all x-values for a graph, while the range is the set of all y-values. For a parabola, the domain is all real numbers and the range is all values less than or equal to 6.5. For a square root function, the domain is all x-values greater than -4 and the range is all y-values greater than 1. For a cubic function, both the domain and range are all real numbers since the graph does not stop anywhere.
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Domain and range from graphs
- 1. Domain and Range Function Properties
- 2. This is a Parabola – the graph of a Quadratic Function It has many properties. The one thing that this parabola has that EVERY OTHER FUNCTION has, is a Domain and Range. The Domain is the set of all the x values that are part of this graph. The Range is the set of all the y values that are part of this graph. The Domain is All Real Numbers because the graph does not stop anywhere on it’s paths left or right. The Range is all values that are less than or equal to 6.5 since that is the highest point the graph will ever reach.
- 3. This is the graph of a square root function. Like the parabola before, it also has a Domain and Range. To find the Domain we will look at the graphs travels left and right. To find the Range we will look at the graphs travels up and down.
- 4. (-4, 1) The vertex of this graph is shown. This happens to be the starting point for this graph. All the x values are to the right (greater than) the x value of -4. All the y values are above (greater than) the y value of 1. Using that information, determine what the Domain and Range of this square root function. When you think you know the answer, move to the next slide.
- 5. (-4, 1) The Domain is 𝑥 ≥ −4. The Range is 𝑦 ≥ 1.
- 6. This is the graph of a Cubic Function. You’ll see that it has a turning point at (2, 3). But that is NOT a starting point for this graph. It is not going to help us determine the left/right and up/down movements of the graph. The graph is moving left and down, and right and up. There is no place that this graph stops or skips. So there are no limitations on the domain or the range. Domain is ALL REAL NUMBERS. Range is ALL REAL NUMBERS.