Math Example--Special Functions--Square Root Functions in Tabular and Graph Form: Example 11

Topic

Radical Functions

Description

This example demonstrates 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, 7) with their corresponding y-values (1, 2, 2.732, 3.236, 3.646). 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 simple vertical shift of the basic square root function. It helps them understand how adding a constant outside the square root 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 adding 1 outside the square root affect the function? How is this different from adding 1 inside the square root?

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