Math Problem Statement

draw the graph of sin |2x-1| +1

Solution

Here is the graph of the function f(x)=sin2x1+1f(x) = \sin{|2x - 1|} + 1. As you can see, the graph is periodic due to the sine function, and it shifts vertically by 1 unit because of the +1+1 term. The absolute value inside the sine function introduces symmetry around x=0.5x = 0.5, creating unique variations in the oscillations.

Would you like any further details or have questions about this graph?

Here are 5 related questions:

  1. What is the period of the function sin2x1+1\sin{|2x - 1|} + 1?
  2. How does the graph of sinx\sin|x| compare to sin2x1+1\sin{|2x - 1|} + 1?
  3. What happens if we replace sin\sin with cos\cos in the function?
  4. How would the graph change if we modified the constant 1 outside the sine function?
  5. Can you find the maximum and minimum values of sin2x1+1\sin{|2x - 1|} + 1?

Tip: The absolute value inside the sine function reflects portions of the graph, impacting symmetry and behavior of the function.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Trigonometry
Absolute Value
Sine Function
Graph Transformations

Formulas

f(x) = sin|2x - 1| + 1

Theorems

Properties of Sine Function
Symmetry in Absolute Value Functions
Periodicity of Trigonometric Functions

Suitable Grade Level

Grades 10-12