C957 Applied Algebra Comprehensive Study Guide & Key Concepts | Questions And Answers, Latest
Update | 100% Correct Answers | Graded
Applied Algebra – C957
Course Planning tool results –
- Linear functions – 70%
- Logistic Functions – 40%
- Validity of Models – 10%
- Graphical Depictions – 100%
- Polynomial Functions – 70%
- Exponential Functions – 10%
- Meanings of Functions – 40%
Input and Output Relationships Cohort
Module 1, 4, 6, 10, 13, 17
Function Notation –
- F (x) – x is input variable, F is output variable
- F (a) = b – F is related to B. B is output as well
- C (State) = Capital
- C (Nevada) = Carson City
- (Input, Output) - (Colorado, Denver)
- The effect is typically the output variable.
- Need to study more on logistic functions
, Key Concepts Sheet
Input and Output –
Function Type –
Linear – Example Function – L(x) = 3x – 5 Substitute 5 in for x – L(5) = 3(5) – 5
Solution - =15-5, = 10
Polynomial – P(x) = -2x2 + 3x + 5, Substitute 5 in for x – P(5) = -2(5)2 + 3(5) + 5
Solution - = 2(25) + 15 – 5, = -50 + 15 – 5, + -40
Exponential – E(x) = 2e-0.5x Substitute 5 in for x – E(x) = 2e-0.5(5)
Solution - =2e-2.5 , = 0.165
Logistic – L(x) = +5e-0.2x Substitute 5 in for x, L(5) = +5-0.2(5)
Solution - = +5e-1 , = 10000/1 +1.84, = 10000/2.84, = 3521.13
- The independent variable is the variable that explains, influences, or affects the other
variables. The independent variable is put on the x-axis, or horizontal axis on a graph.
- The dependent variable is the variable that responds to the independent variable; that is,
the dependent variable responds to change. On a graph, the dependent variable is usually
labeled on the y-axis, which is the vertical axis.
- Working with the graph of a function, points are labeled using ordered pairs. For example,
(3,2) 3 would be the input value of the independent variable, and 2 would be the output
value of the dependent variable.
- Working with an input of time, it is always important to note the starting time and use
military time. For example, if out input is hours after 12am, then 10pm would be
represented as x = 22, not x = 10
- If asked to find f(3) you will find the corresponding output when x = 3. When asked to find
f(x) = 3 you must find the input with corresponding output of 3.
- Know how to use “e” on your calculator.
Rate of Change –
- The average rate of change between points (x1, y1) and (x2,y2) is given by y2-y1/x2-x1
- The instantaneous rate of change measure the rate of change at one specific time.
- For linear equations we always have that the slope is equal to both the average rate of
change and instantaneous rate of change.
- If a function has a negative rate of change, then it is decreasing, and if it has a positive rate
of change then it is increasing.
Concavity –
- Concave Up is shaped like a U and Concave Down is an upside U.
Update | 100% Correct Answers | Graded
Applied Algebra – C957
Course Planning tool results –
- Linear functions – 70%
- Logistic Functions – 40%
- Validity of Models – 10%
- Graphical Depictions – 100%
- Polynomial Functions – 70%
- Exponential Functions – 10%
- Meanings of Functions – 40%
Input and Output Relationships Cohort
Module 1, 4, 6, 10, 13, 17
Function Notation –
- F (x) – x is input variable, F is output variable
- F (a) = b – F is related to B. B is output as well
- C (State) = Capital
- C (Nevada) = Carson City
- (Input, Output) - (Colorado, Denver)
- The effect is typically the output variable.
- Need to study more on logistic functions
, Key Concepts Sheet
Input and Output –
Function Type –
Linear – Example Function – L(x) = 3x – 5 Substitute 5 in for x – L(5) = 3(5) – 5
Solution - =15-5, = 10
Polynomial – P(x) = -2x2 + 3x + 5, Substitute 5 in for x – P(5) = -2(5)2 + 3(5) + 5
Solution - = 2(25) + 15 – 5, = -50 + 15 – 5, + -40
Exponential – E(x) = 2e-0.5x Substitute 5 in for x – E(x) = 2e-0.5(5)
Solution - =2e-2.5 , = 0.165
Logistic – L(x) = +5e-0.2x Substitute 5 in for x, L(5) = +5-0.2(5)
Solution - = +5e-1 , = 10000/1 +1.84, = 10000/2.84, = 3521.13
- The independent variable is the variable that explains, influences, or affects the other
variables. The independent variable is put on the x-axis, or horizontal axis on a graph.
- The dependent variable is the variable that responds to the independent variable; that is,
the dependent variable responds to change. On a graph, the dependent variable is usually
labeled on the y-axis, which is the vertical axis.
- Working with the graph of a function, points are labeled using ordered pairs. For example,
(3,2) 3 would be the input value of the independent variable, and 2 would be the output
value of the dependent variable.
- Working with an input of time, it is always important to note the starting time and use
military time. For example, if out input is hours after 12am, then 10pm would be
represented as x = 22, not x = 10
- If asked to find f(3) you will find the corresponding output when x = 3. When asked to find
f(x) = 3 you must find the input with corresponding output of 3.
- Know how to use “e” on your calculator.
Rate of Change –
- The average rate of change between points (x1, y1) and (x2,y2) is given by y2-y1/x2-x1
- The instantaneous rate of change measure the rate of change at one specific time.
- For linear equations we always have that the slope is equal to both the average rate of
change and instantaneous rate of change.
- If a function has a negative rate of change, then it is decreasing, and if it has a positive rate
of change then it is increasing.
Concavity –
- Concave Up is shaped like a U and Concave Down is an upside U.
