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 , we need to look for the points where the graph crosses the x-axis. The x-intercepts occur where .
From the graph, we can see that the curve crosses the x-axis at the following x-values:
Thus, the x-intercepts are .
Would you like more details, or do you have any questions about this? Here are some related questions:
- What is the significance of x-intercepts in a real-world problem?
- How would you find y-intercepts from a graph?
- What does the slope of the line near the x-intercepts tell you about the function's behavior?
- Can a function have no x-intercepts? If so, under what conditions?
- 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., .
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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