Math Example--Special Functions--Square Root Functions in Tabular and Graph Form: Example 6

Topic

Radical Functions

Description

This example illustrates the function y = √(x + 1). The graph shows an increasing curve that starts at (0, 1) and rises as x increases. A table displays x-y coordinates for x-values of 0, 1, 3, 5, and 7, with y-values ranging from 1 to 2.828. Students are asked to create a table of x-y coordinates and graph the function, which includes the points (0, 1), (1, 1.414), (3, 2), (5, 2.449), and (7, 2.828).

This example introduces students to square root functions with a constant term inside the radical. It helps them understand how adding a positive constant inside the square root affects the graph, shifting it vertically and changing its starting point. By comparing this to the basic y = √(x) function, students can visualize the impact of the constant 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: Now, let's explore 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 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.