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

To find the x-intercepts of the graph of y=f(x)y = f(x), we need to look for the points where the graph crosses the x-axis. The x-intercepts occur where y=0y = 0.

From the graph, we can see that the curve crosses the x-axis at the following x-values:

  • x=11x = -11
  • x=7x = -7
  • x=0x = 0
  • x=3x = 3
  • x=8x = 8
  • x=13x = 13

Thus, the x-intercepts are x=11,7,0,3,8,13x = -11, -7, 0, 3, 8, 13.

Would you like more details, or do you have any questions about this? Here are some related questions:

  1. What is the significance of x-intercepts in a real-world problem?
  2. How would you find y-intercepts from a graph?
  3. What does the slope of the line near the x-intercepts tell you about the function's behavior?
  4. Can a function have no x-intercepts? If so, under what conditions?
  5. How would you algebraically determine the x-intercepts of a given function?

Tip: Remember that x-intercepts are points where the output of the function is zero, i.e., f(x)=0f(x) = 0.

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Math Problem Analysis

Mathematical Concepts

Algebra
Graphing Functions
X-intercepts

Formulas

f(x) = 0 for x-intercepts

Theorems

X-intercepts theorem

Suitable Grade Level

Grades 8-10