Math Problem Statement

ما مدى الدالة الممثلة في الشكل المجاور؟

Solution

The image shows a graph of a function, and the question asks for the range of the function represented in the graph. Let's analyze the graph:

  • The graph seems to be a cubic function with two turning points, and it reaches its minimum and maximum at y=3y = -3 and y=3y = 3 respectively.
  • The question offers four choices for the range:
    1. y0y \geq 0
    2. y4y \geq -4
    3. All real numbers
    4. 3y3-3 \leq y \leq 3

Based on the visual inspection, the function has values ranging from y=3y = -3 to y=3y = 3. Therefore, the correct range of the function is 3y3-3 \leq y \leq 3, which corresponds to choice D.

Would you like more details or have any further questions?

Here are 5 related questions:

  1. What is the domain of the given function?
  2. How do we determine the range of a function graphically?
  3. Can a cubic function have a range of all real numbers?
  4. How does the shape of the graph help in identifying critical points?
  5. How do we calculate turning points for a cubic function?

Tip: The range of a function is the set of all possible output values (y-values) that the function can take. You can find it by looking at the vertical extent of the graph.

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Math Problem Analysis

Mathematical Concepts

Graph Analysis
Range of Functions
Cubic Functions

Formulas

Range of a function based on its graph

Theorems

Range Theorem for Continuous Functions

Suitable Grade Level

Grades 10-12