Math Example--Special Functions--Square Root Functions in Tabular and Graph Form: Example 7

Topic

Radical Functions

Description

This example demonstrates the function y = √(2x + 1). The graph shows an increasing curve starting at (0, 1) and rising more steeply than previous examples as x increases. A table lists x-values (0, 1, 3, 5, and 7) with their corresponding y-values, ranging from 1 to approximately 3.873. Students are asked to create a table of x-y coordinates and graph the function y = √(2x + 1), with x-values of 0, 1, 3, 5, and 7 and corresponding y-values of 1, 1.732, 2.646, 3.317, and 3.873.

This example builds on previous ones, introducing a coefficient inside the square root along with a constant term. It helps students understand how these factors affect the shape, steepness, and starting point of the graph. By comparing this function to earlier examples, students can visualize the impact of the coefficient and constant on the function's behavior.

Providing multiple examples with slight variations is essential for deepening students' understanding of square root functions. It allows them to make connections between different forms and develop a more intuitive grasp of how changes in the equation affect the graph. This approach fosters critical thinking and analytical skills, preparing students for more complex mathematical concepts.

Teacher's Script: Let's examine the function y = √(2x + 1). How do you think this graph will compare to our previous examples? We'll create our table of x-y coordinates using the same x-values as before: 0, 1, 3, 5, and 7. Notice how the y-values are different, especially for x = 0. When we plot these points, we can see that this curve starts at (0, 1) and rises more steeply than y = √(x). Can anyone explain why this happens? How do the coefficient 2 and the constant 1 inside the square root affect the function?

For a complete collection of math examples related to Radical Functions click on this link: Math Examples: Square Root Functions Collection.