Math Problem Statement

Find the range of the function graphed below. Enter your answer as an inequality (e.g., y > 5).

Solution

From the image, we can see that the function is a curve that starts from a certain point on the graph and increases as it moves upwards. The curve seems to have a starting point near y=2y = -2, and it increases without bound.

The range of a function refers to the set of possible yy-values (outputs) that the function can take. In this case, the graph starts at approximately y=2y = -2 and increases infinitely. Therefore, the range can be written as an inequality based on this observation:

y2y \geq -2

This means the function's output values are greater than or equal to 2-2.

Would you like more details or have any further questions?

Here are some related questions to explore:

  1. How is the domain of a function different from its range?
  2. How would the range change if the graph was reflected across the x-axis?
  3. What is the significance of the starting point in determining the range?
  4. How do you find the range of more complex functions (e.g., trigonometric or exponential)?
  5. How can the range of a function be affected by vertical transformations?

Tip: When determining the range from a graph, always look at the smallest and largest yy-values the curve reaches or approaches.

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Math Problem Analysis

Mathematical Concepts

Range of a function
Graph interpretation

Formulas

-

Theorems

Range definition

Suitable Grade Level

Grades 8-10