Math Problem Statement

Refer to the graph of y = f(x) shown to the right. The axes are marked off in one-unit intervals. Find the x-intercepts of f.

Solution

In the image, the problem asks you to find the x-intercepts of the graph y=f(x)y = f(x), where the axes are marked in one-unit intervals.

The x-intercepts are the points where the graph crosses the x-axis, meaning the value of yy is zero at these points. From the graph, we can observe the x-values where y=0y = 0.

Looking closely at the graph:

  • The curve touches the x-axis at x=3x = -3,
  • The curve touches the x-axis at x=5x = 5,
  • The curve touches the x-axis at x=10x = 10,
  • The curve touches the x-axis at x=12x = 12.

Thus, the x-intercepts are x=3,5,10,12x = -3, 5, 10, 12.

The provided solution in the image confirms these intercepts. If you'd like further clarification or more details, let me know!


Do you have any questions or need more details?

Here are some related questions to think about:

  1. What is the general definition of an x-intercept?
  2. How do you determine the x-intercepts of a polynomial function algebraically?
  3. Could there be more than one x-intercept in a real-world application?
  4. How do the x-intercepts help in understanding the behavior of the graph of a function?
  5. How would you find the y-intercept of the graph?

Tip: When working with graphs, always check both x- and y-intercepts to gain insights into the function's behavior.

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Math Problem Analysis

Mathematical Concepts

Graphing Functions
X-Intercepts
Coordinate Geometry

Formulas

X-Intercept Formula: Set y = 0 and solve for x

Theorems

Graph Intercept Theorem

Suitable Grade Level

Grades 8-10