Math Problem Statement

What is the domain and range

Using the graph, identify the domain and range for the function below.

Solution

From the image, we have a graph of a curve that appears to start at (0,6)(0, -6) and extends to the right as xx increases, continuing indefinitely in that direction.

Domain:

The domain refers to the set of all possible xx-values for which the function is defined. Since the curve starts at x=0x = 0 and extends to the right, the domain includes all x0x \geq 0.

Domain: [0,)[0, \infty)

Range:

The range refers to the set of all possible yy-values that the function takes. The curve starts at y=6y = -6 and increases as xx increases. Since the curve continues indefinitely upwards, the range includes all y6y \geq -6.

Range: [6,)[-6, \infty)

Would you like more details, or do you have any questions?

Here are some related questions you can consider:

  1. How would the domain change if the curve started at x=3x = -3 instead of x=0x = 0?
  2. How can you determine the range of a function without a graph?
  3. What is the significance of the domain and range in real-world applications?
  4. How would the range change if the curve approached a maximum yy-value?
  5. Can you identify if this graph represents a specific function type, such as a square root or exponential function?

Tip: Always check for any restrictions on the xx-values or yy-values when determining domain and range from a graph.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Domain
Range
Graphs of Functions

Formulas

-

Theorems

-

Suitable Grade Level

Grades 9-11