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Questions and Answers
What is a function in the context of mathematics?
What is a function in the context of mathematics?
- A relationship where each input has one and only one output. (correct)
- A relationship where inputs have different outputs every time.
- A set of x-values and y-values with multiple outputs for each input.
- A set of unrelated inputs and outputs.
Which of the following sets of ordered pairs represents a function?
Which of the following sets of ordered pairs represents a function?
- {(3,4), (4,-3), (7,4), (3,8)}
- {(6,-5), (7,-3), (8,-1), (9,1)} (correct)
- {(2,-2), (5,9), (5,-7), (1,4)}
- {(9,5), (10,5), (9,-5), (10,-5)}
Consider the following table of time (in minutes) vs. temperature (°C). Does this relationship represent a function?
Consider the following table of time (in minutes) vs. temperature (°C). Does this relationship represent a function?
- No, because the increase in temperature is not constant over time.
- Yes, because each minute has a unique temperature. (correct)
- No, because the minutes are higher than the temperature.
- Yes, because as time passes, the temperature is consistently increasing.
Four students were asked to describe how to determine if a relation is a function. Which student's statement is NOT entirely correct?
Four students were asked to describe how to determine if a relation is a function. Which student's statement is NOT entirely correct?
Which of the following relations is NOT a function?
Which of the following relations is NOT a function?
Given the function $f(x) = x^2$, evaluate $f(-8)$.
Given the function $f(x) = x^2$, evaluate $f(-8)$.
Given the function $f(x) = -2x^2 + 1$, evaluate $f(-3)$.
Given the function $f(x) = -2x^2 + 1$, evaluate $f(-3)$.
Using the mapping diagram, determine the value of $f(2)$.
Using the mapping diagram, determine the value of $f(2)$.
Given $f(x) = 3x + 2$ and $g(x) = 4 - 5x$, find $(f + g)(x)$.
Given $f(x) = 3x + 2$ and $g(x) = 4 - 5x$, find $(f + g)(x)$.
Given $f(x) = 3x + 2$ and $g(x) = 4 - 5x$, find $(\frac{f}{g})(x)$.
Given $f(x) = 3x + 2$ and $g(x) = 4 - 5x$, find $(\frac{f}{g})(x)$.
What is the domain of a relation?
What is the domain of a relation?
What is the range of a relation?
What is the range of a relation?
Which of the following statements accurately describes the vertical line test?
Which of the following statements accurately describes the vertical line test?
Which of the following set of values is a function?
Which of the following set of values is a function?
According to the table, does the relationship represent a function?
According to the table, does the relationship represent a function?
Refer to the image below (-7 --> 3, 11 --> 5, 11 --> 8 ). Is the relation a function? Why?
Refer to the image below (-7 --> 3, 11 --> 5, 11 --> 8 ). Is the relation a function? Why?
If f(x) = 2 + x - $x^2$, find f(2).
If f(x) = 2 + x - $x^2$, find f(2).
If g(a) = 3a - 2, find g(1).
If g(a) = 3a - 2, find g(1).
If p(a) = $-43^a$, find p(1).
If p(a) = $-43^a$, find p(1).
If f(x) = $x^2$-3x, find f(-8)
If f(x) = $x^2$-3x, find f(-8)
If h(n) = $-2n^2$ + 4, find h(4)
If h(n) = $-2n^2$ + 4, find h(4)
Find (f + g)(x) given f(x)=3x+3 and g(x)=-4x+1.
Find (f + g)(x) given f(x)=3x+3 and g(x)=-4x+1.
Find (f + g)(x) given f(x)=2x+5 and g(x)=4+2x-2.
Find (f + g)(x) given f(x)=2x+5 and g(x)=4+2x-2.
Find (f + g)(x) given f(x)= −15-2x+5 and g(x)=3+ x-7
Find (f + g)(x) given f(x)= −15-2x+5 and g(x)=3+ x-7
What is the process of 'subtrahend' in the context of integer subtraction?
What is the process of 'subtrahend' in the context of integer subtraction?
Find (f - g)(x) given f(x)=-15x^3-2x+5 and g(x)=3x^2+x-7.
Find (f - g)(x) given f(x)=-15x^3-2x+5 and g(x)=3x^2+x-7.
Determine the correct rule when multiplying integers with like signs.
Determine the correct rule when multiplying integers with like signs.
Select the correct rule when multiplying integers with unlike signs.
Select the correct rule when multiplying integers with unlike signs.
Given f(x)=3x and g(x)=-4x+1, find (f * g)(x).
Given f(x)=3x and g(x)=-4x+1, find (f * g)(x).
Which of the following expressions accurately represents the quotient of two functions, f(x) and g(x)?
Which of the following expressions accurately represents the quotient of two functions, f(x) and g(x)?
Given f(x) = 3x - 15 and g(x) = -6x + 12, find (f/g)(x).
Given f(x) = 3x - 15 and g(x) = -6x + 12, find (f/g)(x).
How is 'composition of functions' best described?
How is 'composition of functions' best described?
What expression represents the composition of function f with function g, denoted as 'f of g'?
What expression represents the composition of function f with function g, denoted as 'f of g'?
Given the functions f(x)=3x+2 and g(x)=x-4, find (f o g)(x).
Given the functions f(x)=3x+2 and g(x)=x-4, find (f o g)(x).
A cable company charges a $500 monthly cable connection fee plus $125 for each hour of pay-per-view (PPV) events. If a customer watches 25 hours of PPV in one month, what is the total monthly bill?
A cable company charges a $500 monthly cable connection fee plus $125 for each hour of pay-per-view (PPV) events. If a customer watches 25 hours of PPV in one month, what is the total monthly bill?
If there is a $7 fixed charge and price per kilometer is $2, create an equation to model traveling x kilometers.
If there is a $7 fixed charge and price per kilometer is $2, create an equation to model traveling x kilometers.
Flashcards
Sets
Sets
A collection of well-defined, distinct objects sharing a common characteristic.
Relation
Relation
A rule relating values from one set (domain) to another (range); a set of ordered pairs (x, y).
Domain
Domain
All possible x or input values in a relation or function.
Range
Range
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Ordered Pair
Ordered Pair
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Function
Function
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Mapping
Mapping
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Graphing Functions
Graphing Functions
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Evaluate a function
Evaluate a function
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Adding Functions
Adding Functions
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Subtracting Functions
Subtracting Functions
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Multiplying Functions
Multiplying Functions
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Dividing functions
Dividing functions
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Composition of Functions
Composition of Functions
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What does the function say?
What does the function say?
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Study Notes
- The lesson aims to determine functions and relations, illustrate functions through mapping diagrams, sets, and graphs, and represent real-life situations using functions
Sets
- Sets comprise well-defined and distinct objects, known as elements, that possess a shared characteristic
Relation
- Relation involves a rule connecting values from one set, called the domain, to another set, called the range.
- Relation includes a set of ordered pairs (x,y)
Domain and Range
- Domain represents the set of all x or input values.
- Range represents the set of all y or output values.
Ordered Pair
- Ordered Pair is a pair of objects in a specific order
- An ordered pair lists two members in order, separated by a comma, enclosed in parentheses (Aggarwal, 2014)
Function
- Function refers to a set of ordered pairs, where each x-value corresponds to only one y-value
- Functions can be shown via set notation, mapping, and graphs
Mapping
- Mapping illustrates element pairings, similar to a flowchart, displaying input and output values.
- In Mapping, a function requires that no x-value have multiple pairs (Varsity Tutors, n.d.).
Sets
- In sets, functions are lists of comma-separated elements within curly braces, with x-values not being repeated.
Vertical Line Test
- Vertical Line Test (VLT) is used in graphing.
- VLT creates imaginary vertical lines across a graph, where the line hits only one point for the graph to be a function.
Real Life Examples
- Circle's circumference (C) is a function of its diameter (d), C(d).
- Shadow's length (L) relates to a person's height (h), L(h).
- Driving location (D) relates to time (t), D(t).
- Temperature (F) is based on factors or inputs (t), F(t).
- Available money (A) relates to earning time (t), A(t).
Evaluating Functions
- Evaluate a function by replacing/substituting its variables with a given number of expressions.
Operations of functions
- The sum of functions can be written as f(x)+g(x) or (f+g)(x).
Integer Addition
- To add integers with unlike signs use the sign of the larger number
Integer Subtraction
- Rule: In subtracting integers, change the sign of subtrahend and proceed to addition.
Function Subtraction
- The difference of functions can be written as f(x)-g(x) or (f-g)(x).
Multiplying Integers
- The product of two like signs is always positive; the product of two unlike signs is always negative
Multiplying Functions
- Product of functions can be written as f(x)•g(x) or (f•g)(x) or (fg)(x)
Division of Integers
- The quotient of two like signs integers is always positive
- The quotient of two unlike signs integers is always negative
Dividing Functions
- The quotient of functions can be writtef(x) ÷ g(x) or (f/g)(x) = f(x)/g(x)
Composition of Functions
- Composition Function refers to combining two or more functions where the output from one becomes the input for the next
- The composition of functions can be written as (f o g)(x)=f(g(x))
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