Math Example--Special Functions--Square Root Functions in Tabular and Graph Form: Example 16

Topic

Radical Functions

Description

This example illustrates the function y = √(x + 1) + 1. The graph shows an increasing curve starting at (0, 2) and rising as x increases. A table lists x-values (0, 1, 3, 5, and 7) with their corresponding y-values (2, 2.414, 3, 3.449, and 3.828). Students are asked to create a table of x-y coordinates and graph the function, which includes these points.

This example introduces students to a square root function with both a constant term inside and outside the radical. It helps them understand how these factors affect the shape, starting point, and vertical shift of the graph. By comparing this to previous examples, students can visualize the combined impact of the constants on the function's behavior.

Providing multiple examples with different variations is essential for deepening students' understanding of square root functions. Each example builds on previous knowledge, challenging students to apply what they've learned in new contexts. This approach helps students recognize patterns and relationships between equations and their graphs, fostering critical thinking and analytical skills.

Teacher's Script: Let's examine the function y = √(x + 1) + 1. How do you think this graph will differ from our previous examples? We'll use 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, 2) instead of the origin. Can anyone explain why this happens? How does adding 1 inside the square root affect the function, and how is this different from adding 1 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.