Math Example--Special Functions--Square Root Functions in Tabular and Graph Form: Example 17

Topic

Radical Functions

Description

This example demonstrates the function y = √(2x + 1) + 1. The graph shows an increasing curve starting at (0, 2) and rising more steeply than the previous example as x increases. A table lists x-values (0, 1, 3, 5, 7) with their corresponding y-values (2, 2.732, 3.646, 4.317, 4.873). Students are asked to create a table of x-y coordinates and graph the function, which includes these points.

This example builds on the previous one, introducing a coefficient inside the square root along with constant terms inside and outside. It helps students understand how these factors affect the shape, steepness, and starting point of the graph. By comparing this function to y = √(x + 1) + 1, students can visualize the impact of the coefficient 2 on the function's behavior while maintaining the vertical shift.

Providing a range of examples with different coefficients and constants is essential for developing a deep understanding of square root functions. Each example challenges students to apply what they've learned in new contexts, fostering critical thinking and analytical skills. This approach helps students recognize patterns and relationships between equations and their graphs, preparing them for more complex mathematical concepts.

Teacher's Script: Now, let's look at the function y = √(2x + 1) + 1. How do you think this graph will compare to our previous example, y = √(x + 1) + 1? We'll use the same x-values: 0, 1, 3, 5, and 7. Notice how the y-values are larger this time, except for x = 0. When we plot these points, we can see that this curve starts at (0, 2) like the previous example, but rises more steeply. Can anyone explain why this happens? How does the coefficient 2 inside the square root affect the function, and how is this different from adding 1 inside and outside the square root?

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