Podcast
Questions and Answers
Which representation of a function provides a visual interpretation of the relationship?
Which representation of a function provides a visual interpretation of the relationship?
- Verbal (Words)
- Algebraic (Formula)
- Numerical (Table)
- Graphical (correct)
What does the formula A = f(t) = 1000(1.03)^t represent in terms of a banking scenario?
What does the formula A = f(t) = 1000(1.03)^t represent in terms of a banking scenario?
- The cumulative interest earned
- The total amount in the account after t years (correct)
- The annual percentage increase
- The initial deposit amount
Which of the following functions does NOT represent y as a function of x?
Which of the following functions does NOT represent y as a function of x?
- x^2 + y^2 = 1 (correct)
- y = 5 - 2x
- y = x^2 - 4
- y = 2x + 3
Which condition must be met for a graph to be classified as a function?
Which condition must be met for a graph to be classified as a function?
In the bank account example, if t = 3 years, what is the value of A?
In the bank account example, if t = 3 years, what is the value of A?
What does the domain of a function refer to?
What does the domain of a function refer to?
According to the vertical line test, which of the following graphs indicates that a relation is a function?
According to the vertical line test, which of the following graphs indicates that a relation is a function?
If A = f(t) represents a function, which part of the expression signifies the dependent variable?
If A = f(t) represents a function, which part of the expression signifies the dependent variable?
Which statement correctly describes the relationship between x and y in a function?
Which statement correctly describes the relationship between x and y in a function?
What is the value of h(3) if h(x) = 5(x - 2)² + 1?
What is the value of h(3) if h(x) = 5(x - 2)² + 1?
What is f(-2) if f(x) = 3x² + x - 1?
What is f(-2) if f(x) = 3x² + x - 1?
How is f(x) described in terms of its different parts in a piecewise function?
How is f(x) described in terms of its different parts in a piecewise function?
What is the value of g(8) if g(x) is defined as g(x) = {−x, x < −2; 1, −2≤x}?
What is the value of g(8) if g(x) is defined as g(x) = {−x, x < −2; 1, −2≤x}?
For the equation f(x) = -2, which of the following is likely the correct approach to solving for x?
For the equation f(x) = -2, which of the following is likely the correct approach to solving for x?
What is the primary purpose of defining a function in mathematical terms?
What is the primary purpose of defining a function in mathematical terms?
If h(-2) is to be solved from h(x) = -4x + 1, what is the resulting value?
If h(-2) is to be solved from h(x) = -4x + 1, what is the resulting value?
Flashcards
Function
Function
A rule that assigns each input value exactly one output value.
Domain
Domain
The set of all possible input values (x-values) of a function.
Range
Range
The set of all possible output values (y-values) of a function.
Vertical Line Test
Vertical Line Test
Signup and view all the flashcards
Function Representation
Function Representation
Signup and view all the flashcards
Function Formula
Function Formula
Signup and view all the flashcards
Graph of a function
Graph of a function
Signup and view all the flashcards
Numerical Representation
Numerical Representation
Signup and view all the flashcards
Is y a function of x?
Is y a function of x?
Signup and view all the flashcards
Independent Variable
Independent Variable
Signup and view all the flashcards
Dependent Variable
Dependent Variable
Signup and view all the flashcards
f(x)
f(x)
Signup and view all the flashcards
Piecewise function
Piecewise function
Signup and view all the flashcards
Function notation f(x)
Function notation f(x)
Signup and view all the flashcards
Solving for x in a function
Solving for x in a function
Signup and view all the flashcards
Evaluating a function
Evaluating a function
Signup and view all the flashcards
Study Notes
Representing Functions
- Functions describe how one quantity depends on another.
- Functions can be represented in words, formulas, graphs, or tables.
Verbal Representation (Words)
- Example: Depositing $1000 in a bank account with 3% annual interest. The amount (A) in t years can be described as A = f(t) = 1000(1.03)t.
Algebraic Representation (Formula)
- A = f(t) = 1000(1.03)t, where A is the amount after t years.
Graphical Representation
- Visual representation of the function's relationship.
- Shows how the output value changes with the input value.
- Example: A graph showing the amount of money in the account (A) versus the number of years (t).
Numerical Representation (Table)
- Table of input (independent variable) and output (dependent variable) values.
- Example: A table showing the amount of money (A) in the account for different years (t).
Function Definition
- A function assigns each input value in the domain to exactly one output value in the range.
Example 1: Determining if a formula describes y as a function of x.
- Assess if each input (x) value produces exactly one output (y) value.
- Example: x² + y² = 1 does not represent y as a function of x.
Vertical Line Test for Functions
- Every vertical line intersects a graph at most once to represent a function.
Dependent and Independent Variables
- Independent variable (x): Input value.
- Dependent variable (y): Output value, determined by the input.
Function Notation
- y = f(x) means y is a function of x.
- f(x) is the output value when the input is x.
Example 2: Evaluating Functions
- Given a function and an input, compute the output value.
- Example: If h(x) = 5(x − 2)² + 1, find h(3).
Example 3: Using Functions
- Evaluate functions, including given graphs, tables or formulas.
- Example: Find f(-2), g(-2), h(-2), solve f(x) = −2 for x.
Piecewise Defined Functions
- A function defined by multiple formulas, each applicable over a particular part of the domain.
- Example: f(x)=
3-x, if x<-1 12x, if x≧-1
- Evaluate using the formula appropriate to the input value's position in the domain.
Domain and Range of Functions
- Domain: Set of all possible input values (x-values).
- Range: Set of all possible output values (y-values).
- Example: Find the domain of f(x)=
x+5
- ----
x-2
- Find the range of g(x)=x² + a .
Example 4: Piecewise Functions, evaluation with given input
Example 5: Simplifying function expressions
- Simplify composed functions
- Example: If f(x)=x²+2x, find
(f(x+h) - f(x)) / h
Example 6: Finding domain and range from a graph
Example 7: Finding the domains of different functions.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.