What are the domain and range…

Mathematics Questions

What are the domain and range of the function provided below?

Short Answer

The graph has a y-intercept of -5 and an x-intercept of 5, indicating it is a straight line with a positive slope. Both the domain and range of the function are all real numbers, represented as x = R and y = R, respectively.

Step-by-Step Solution

Step 1: Identify the Graph Characteristics

Analyze the graph which shows a curve with specific intercepts. The y-intercept is at -5, and the x-intercept is at 5. This helps to outline the basic properties of the graph that will define its behavior.

  • Y-intercept: -5
  • X-intercept: 5
  • Graph Type: Straight line with a positive slope

Step 2: Determine the Domain of the Function

The domain refers to all possible values of x for which the function is defined. Since the graph is continuous without breaks, it indicates that x can take any real number. Thus, the domain can be expressed as all real numbers.

  • Domain: x = R
  • Values of x: From -‚àû to +‚àû

Step 3: Determine the Range of the Function

The range represents all possible values of y associated with the function. As with the domain, the graph demonstrates continuity, allowing y to also take any value within the real number spectrum. Therefore, the range can similarly be established as all real numbers.

  • Range: y = R
  • Values of y: From -‚àû to +‚àû

Related Concepts

Y-intercept

The point where the graph intersects the y-axis, indicating the value of y when x is 0.

X-intercept

The point where the graph intersects the x-axis, indicating the value of x when y is 0.

Domain

The set of all possible input values (x) for which a function is defined, usually expressed in set notation.

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