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Questions and Answers
What is the set of input values for which a function is defined?
What does f(x) = y mean?
What is the purpose of graphing a function?
What is the general form of a linear function?
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What does the slope of a linear function represent?
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What is the process of building a function to model a realworld situation or satisfy certain conditions?
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What is the set of output values that a function can produce?
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What does the yaxis represent in a graph of a function?
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What is the point where a linear function crosses the yaxis?
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What is the characteristic of a linear function that represents the rate of change?
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Study Notes
Domain and Range

Domain: The set of input values (x) for which a function is defined.
 Expressed as {x  x is an element of the domain}
 May be all real numbers, or a subset of real numbers

Range: The set of output values (y) that a function can produce.
 Expressed as {y  y is an element of the range}
 May be all real numbers, or a subset of real numbers
Function Notation

Function notation: A way to express a function using variables and parentheses.
 f(x) is read as "f of x"
 f(x) = y means "f assigns to x the value y"
 Example: f(x) = 2x + 1
Graphing Functions

Graphing a function: Plotting the points (x, y) that satisfy the function.
 The graph of a function is a visual representation of the relationship between x and y.
 The xaxis represents the domain, and the yaxis represents the range.
 Graphing helps identify key features, such as maxima, minima, and asymptotes.
Linear Functions

Linear function: A function with a constant rate of change.
 General form: f(x) = mx + b, where m is the slope and b is the yintercept.
 Characteristics:
 The graph is a straight line.
 The slope (m) represents the rate of change.
 The yintercept (b) is the point where the line crosses the yaxis.
Constructing Functions

Constructing a function: Building a function to model a realworld situation or satisfy certain conditions.
 Steps:
 Identify the problem or situation.
 Determine the type of function needed (e.g., linear, quadratic, etc.).
 Choose a function that satisfies the conditions.
 Example: Construct a function that models the cost of producing x units of a product, where the cost is $5 per unit plus a fixed overhead of $100.
 Steps:
Domain and Range
 Domain: the set of input values (x) for which a function is defined
 Domain notation: {x  x is an element of the domain}
 Range: the set of output values (y) that a function can produce
 Range notation: {y  y is an element of the range}
Function Notation
 Function notation: a way to express a function using variables and parentheses
 f(x) is read as "f of x"
 f(x) = y means "f assigns to x the value y"
 Example: f(x) = 2x + 1
Graphing Functions
 Graphing a function: plotting the points (x, y) that satisfy the function
 The graph of a function is a visual representation of the relationship between x and y
 The xaxis represents the domain, and the yaxis represents the range
 Graphing helps identify key features, such as maxima, minima, and asymptotes
Linear Functions
 Linear function: a function with a constant rate of change
 General form: f(x) = mx + b, where m is the slope and b is the yintercept
 Characteristics:
 The graph is a straight line
 The slope (m) represents the rate of change
 The yintercept (b) is the point where the line crosses the yaxis
Constructing Functions
 Constructing a function: building a function to model a realworld situation or satisfy certain conditions
 Steps:
 Identify the problem or situation
 Determine the type of function needed (e.g., linear, quadratic, etc.)
 Choose a function that satisfies the conditions
 Example: modeling the cost of producing x units of a product, where the cost is $5 per unit plus a fixed overhead of $100
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Description
Understand the concepts of Domain and Range in Algebra, including function notation and its applications.