Math Example--Special Functions--Square Root Functions in Tabular and Graph Form: Example 21

Topic

Radical Functions

Description

This example illustrates the function y = √(x) - 1. The graph shows an increasing curve starting at (0, -1) and rising as x increases. A table lists x-values (0, 1, 3, 5, and 7) with their corresponding y-values (-1, 0, 0.732, 1.236, and 1.646). 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 a vertical shift downward. It helps them understand how subtracting a constant outside the radical affects the graph, shifting it vertically without changing its shape. By comparing this to the basic y = √(x) function, students can visualize the impact of the constant on the function's behavior and starting point.

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. How do you think this graph will differ from our first example, y = √(x)? 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, -1) instead of the origin. Can anyone explain why this happens? How does subtracting 1 outside 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.