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Questions and Answers
What is the graph of the equation $x = y^2 + 5$ based on the following points?
What is the graph of the equation $x = y^2 + 5$ based on the following points?
- Graph 1 (correct)
- Graph 4
- Graph 3
- Graph 2
What is the graph of the equation $y = -2x^3$ based on the following points?
What is the graph of the equation $y = -2x^3$ based on the following points?
- Graph 4
- Graph 1
- Graph 3
- Graph 2 (correct)
Does the following table specify a function? Domain Range: (4, 3), (8, 6), (12, 5)
Does the following table specify a function? Domain Range: (4, 3), (8, 6), (12, 5)
True (A)
Does the following table specify a function? Domain Range: (-11, 20), (-18, 17), (-17, -13), (7, -5)
Does the following table specify a function? Domain Range: (-11, 20), (-18, 17), (-17, -13), (7, -5)
Does the given graph specify a function?
Does the given graph specify a function?
Does the given graph specify a function?
Does the given graph specify a function?
Does the equation $2xy = 9$ represent y as a function of x?
Does the equation $2xy = 9$ represent y as a function of x?
What type of function is specified by the equation $y = 6x + rac{1}{2}(3 - 12x)$?
What type of function is specified by the equation $y = 6x + rac{1}{2}(3 - 12x)$?
Determine $y$ to the nearest integer for $y = f(3)$ based on the graph of function $f$.
Determine $y$ to the nearest integer for $y = f(3)$ based on the graph of function $f$.
What are the values of $x$ such that $f(x) = 0$?
What are the values of $x$ such that $f(x) = 0$?
What is the domain of the function $F(x) = 4x^3 + 2x^2$?
What is the domain of the function $F(x) = 4x^3 + 2x^2$?
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Study Notes
Graphs and Functions
- For the function ( x = y^2 + 5 ), points used for graphing include (5, 0), (6, 1), (6, -1), (7, 1.41), and (7, -1.41). Use point-by-point plotting for visualization.
- The function ( y = -2x^3 ) is graphed using points (-2, 16), (-1, 2), (0, 0), (1, -2), and (2, -16), illustrating the shape and behavior of cubic functions.
Function Specifications
- The provided table indicates that a function is defined for inputs (domain) of 4, 8, and 12, yielding outputs (range) of 3, 6, and 5 respectively, validating it as a function.
- In contrast, another table shows inputs (-11, -18, -17, 7) that produce varied outputs (20, 17, -13, -5); since -17 maps to two different outputs, this does not qualify as a function.
Graphical Function Identification
- Certain graphs can indicate whether a function exists, with one graph confirming it does specify a function while another shows it does not, adhering to the vertical line test for functions.
Functional Representation
- The equation ( 2xy = 9 ) displays y as a function of x, affirmatively establishing a relationship between the two variables.
- A specific linear function is identified through the equation ( y = 6x + \frac{1}{2}(3 - 12x) ), indicating it is linear, constant, or neither.
Evaluating Function Values
- For the function graph ( f ), evaluate ( y = f(3) ) where ( y ) approximates to -7 based on graphical representation.
- The value of ( x ) where ( f(x) = 0 ) is found at x = -5, 0, and 8, determining the points where the function intersects the x-axis.
Domain of Functions
- The domain of the cubic function ( F(x) = 4x^3 + 2x^2 ) is identified as ( (-\infty, \infty) ), implying it encompasses all real numbers.
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