Math Problem Statement

Find the domain and range

Find the domain and range of the graph.

Solution

The graph you uploaded represents a sinusoidal curve, which appears to be a standard sine or cosine function. Let’s analyze the domain and range.

  1. Domain: The domain of the sine or cosine function is all real numbers, since the function continues infinitely in both the positive and negative directions along the xx-axis. Domain:(,)\text{Domain}: (-\infty, \infty)

  2. Range: The range of the sine or cosine function is limited between the maximum and minimum values that the curve reaches on the yy-axis. From the graph, the curve oscillates between y=1y = 1 and y=1y = -1. Range:[1,1]\text{Range}: [-1, 1]

So, the domain is all real numbers, and the range is from 1-1 to 11.

Would you like more details or have any questions about this?

Here are 5 related questions you might find interesting:

  1. What is the period of this sinusoidal function?
  2. How do amplitude and phase shift affect the sine or cosine graph?
  3. What is the general equation of a sinusoidal function?
  4. Can this graph represent a real-world phenomenon? If yes, which one?
  5. How would this graph change if the amplitude were doubled?

Tip: Always check the amplitude, period, and phase shift when analyzing or sketching sinusoidal graphs!

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Math Problem Analysis

Mathematical Concepts

Trigonometry
Functions

Formulas

y = sin(x)
y = cos(x)

Theorems

Properties of sine and cosine functions

Suitable Grade Level

Grades 9-12