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Questions and Answers
What is the vertex of the parabola representing the water flow from the sprinkler?
What is the vertex of the parabola representing the water flow from the sprinkler?
What does the negative sign attached to the squared variable indicate about the parabola?
What does the negative sign attached to the squared variable indicate about the parabola?
What does finding the roots of the parabola help determine?
What does finding the roots of the parabola help determine?
What does the maximum height of the water, 4.5 feet from the ground, represent in the graph of the function?
What does the maximum height of the water, 4.5 feet from the ground, represent in the graph of the function?
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What is the definition of a function in math?
What is the definition of a function in math?
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What does the notation $f(x)$ represent in a function?
What does the notation $f(x)$ represent in a function?
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In the function $f(x) = x^2 + 3x - 5$, what does the variable $x$ represent?
In the function $f(x) = x^2 + 3x - 5$, what does the variable $x$ represent?
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What is the domain of the function $f(x) = rac{1}{(x-2)(x+3)}$?
What is the domain of the function $f(x) = rac{1}{(x-2)(x+3)}$?
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Which type of function has a graph representing a constant rate of change?
Which type of function has a graph representing a constant rate of change?
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What is the range of the function $g(x) = x^2 - 4x + 4$?
What is the range of the function $g(x) = x^2 - 4x + 4$?
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Study Notes
Function Domain and Range Summary
- The domain of a function is the set of all possible input values, while the range is the set of all possible output values.
- A function's domain can be restricted by rules such as avoiding zero in a denominator or negative numbers under an even radical.
- Functions can be graphed on a coordinate plane by choosing input values, calculating outputs, and plotting points.
- Linear functions are in the form y = mx + b and have a graph that is a straight line representing constant rate of change.
- Non-linear functions have graphs that follow specific patterns, such as parabolas for even exponent functions and up-down-up or down-up-down patterns for odd exponent functions.
- The graph of a function can reveal its domain and range.
- Example 1: The linear function f(x) = 2x + 3 has a graph that is a straight line with a domain and range of all real numbers.
- Example 2: The non-linear function g(x) = 1/(x-3) has a graph that is a curve with a domain of all real numbers except 3 and a range of all real numbers except 0.
- Example 1: A function f(h) = 12h + 25 represents the amount a student can earn per week with a domain of 0 <= h <= 40 and a range of $25 to $505 per week.
- Example 2: The height of water from a sprinkler is a function with time as the independent variable and height as the dependent variable, following a parabolic path.
- The height function of the water from the sprinkler can be graphed to show its path over time.
- The domain and range of a function can have real-world context, such as the hours worked for earnings or time released for water height.
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Description
Test your understanding of function domain and range with this quiz. Explore the concepts of domain restriction, graphing functions, linear and non-linear functions, and real-world applications.
