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Questions and Answers
What is the key distinction of a function compared to a general relation?
What is the key distinction of a function compared to a general relation?
- Each x value pairs with exactly one y value. (correct)
- All y values must be unique in a function.
- The x values can be repeated in the ordered pairs.
- Each x value can pair with multiple y values.
Which set is correctly identified as belonging to the domain of a relation?
Which set is correctly identified as belonging to the domain of a relation?
- The independent variable values in the ordered pairs. (correct)
- The outcomes dependent on the input values.
- All y values that correspond to each x value.
- The set of possible outputs from the relation.
In the context of a function, how is the range best described?
In the context of a function, how is the range best described?
- It represents the set of possible x values.
- It is an arbitrary selection of y values related to x values.
- It consists of y values that do not depend on x.
- It includes all outputs from the function pertaining to the domain. (correct)
Which statement accurately reflects the relationship between values in a function?
Which statement accurately reflects the relationship between values in a function?
Which term best describes the set of y values in a relation?
Which term best describes the set of y values in a relation?
Which of the following equations represents a linear function?
Which of the following equations represents a linear function?
What is the ordered pair solution for the equation $y = 2x + 4$ when $x = 2$?
What is the ordered pair solution for the equation $y = 2x + 4$ when $x = 2$?
From the equation $3Y - X - 6 = 0$, what is the slope when rewritten in slope-intercept form?
From the equation $3Y - X - 6 = 0$, what is the slope when rewritten in slope-intercept form?
If an ordered pair (x, y) satisfies the equation $y = 2x + 4$, which of the following pairs is NOT a solution?
If an ordered pair (x, y) satisfies the equation $y = 2x + 4$, which of the following pairs is NOT a solution?
What is the characteristic of the graph of a non-linear function?
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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