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Questions and Answers
What is the key distinction of a function compared to a general relation?
Which set is correctly identified as belonging to the domain of a relation?
In the context of a function, how is the range best described?
Which statement accurately reflects the relationship between values in a function?
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Which term best describes the set of y values in a relation?
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Which of the following equations represents a linear function?
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What is the ordered pair solution for the equation $y = 2x + 4$ when $x = 2$?
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From the equation $3Y - X - 6 = 0$, what is the slope when rewritten in slope-intercept form?
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If an ordered pair (x, y) satisfies the equation $y = 2x + 4$, which of the following pairs is NOT a solution?
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What is the characteristic of the graph of a non-linear function?
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Study Notes
Linear Functions
- Linear functions are represented by straight lines on a graph.
- A linear equation can be written in the form $y = mx + c$, where m is the slope and c is the y-intercept.
- An ordered pair (x, y) represents a solution to the function.
- Example: The ordered pair (1, 6) is a solution to the function $y = 2x + 4$.
Coordinate Plane
- The coordinate plane is a two-dimensional space formed by two perpendicular lines called the x-axis and the y-axis.
- It helps in visualizing and plotting points represented by ordered pairs (x, y).
Relations and Functions
- A relation is a pairing of numbers in one set with numbers from another set. It can be represented as a set of ordered pairs.
- The domain of a relation is the set of all x-values (inputs).
- The range of a relation is the set of all y-values (outputs).
- A function is a special type of relation where each x-value corresponds to exactly one y-value.
Function Notation
- Function notation is a way to write equations that emphasizes the relationship between input and output.
- It uses the symbol f(x) to represent the output of the function for a given input x.
- Example: The equation y = -3x + 1 can be written in function notation as f(x) = -3x + 1.
X-intercept and Y-intercept
- The x-intercept is the point where the graph of a function crosses the x-axis. The y-value is 0 at this point.
- The y-intercept is the point where the graph of a function crosses the y-axis. The x-value is 0 at this point.
Standard Form
- An equation in the form ax + by = c is called the standard form of a linear equation.
- To find the x-intercept, set y equal to 0 and solve for x.
- To find the y-intercept, set x equal to 0 and solve for y.
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Description
This quiz covers the fundamental concepts of linear functions, the representation of equations, and the coordinate plane. You'll explore how ordered pairs relate to functions and gain insight into domain and range. Test your understanding of relations, functions, and function notation.
