Math Problem Statement
Identify the x- and y-intercepts of the functions graphed below.
Solution
To solve this, let's identify the x-intercepts and y-intercepts of the graphs one by one.
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Graph 1:
- x-intercept(s): The graph crosses the x-axis at approximately .
- y-intercept: The graph crosses the y-axis at approximately .
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Graph 2:
- x-intercept(s): The graph crosses the x-axis at two points, approximately at and .
- y-intercept: The graph crosses the y-axis at .
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Graph 3:
- x-intercept(s): No x-intercept, the graph does not touch or cross the x-axis.
- y-intercept: The graph crosses the y-axis at approximately .
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Graph 4:
- x-intercept(s): The graph crosses the x-axis at and .
- y-intercept: The graph crosses the y-axis at .
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Graph 5:
- x-intercept(s): No x-intercept.
- y-intercept: No y-intercept.
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Graph 6:
- x-intercept(s): The graph crosses the x-axis at .
- y-intercept: The graph crosses the y-axis at .
Would you like a more detailed breakdown for any of these? Here are some relative questions to expand your understanding:
- What are the properties of functions that don't have x-intercepts or y-intercepts?
- How can we determine the number of x-intercepts of a quadratic function by looking at its equation?
- What are the differences between linear and nonlinear functions in terms of intercepts?
- Can a graph have more than one y-intercept? Why or why not?
- How do you find intercepts algebraically if the function's equation is given?
Tip: A function's x-intercept(s) can be found by setting , while the y-intercept is found by setting .
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Math Problem Analysis
Mathematical Concepts
Functions
Intercepts
Graph Analysis
Formulas
y = f(x)
Theorems
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Suitable Grade Level
Grades 8-10