Standards and EQ'sEQ #1: How can you identify and represent functions? MAFS.912.F-IF.1.1
EQ #2: How can you represent, name, and solve a function? MAFS.912.FIF.1.2, MAFS.912.F-IF.2.5 EQ #3: How do you add and subtract functions? MAFS.912.A-APR.1.1, MAFS.912.A-SSE.1.1 EQ #4: How do you multiply functions? MAFS.912.A-APR.1.1, MAFS.912.A-SSE.1.1 EQ #5: How do you divide functions? MAFS.912.A-APR.1.1, MAFS.912.AS-SE.1.1 EQ #6: How do you apply the closure properties when adding, subtracting, multiplying, and dividing polynomials? MAFS.912.A-CED.1.3 EQ #7: How do you know if a graph is a function? MAFS.912.F-IF.2.4 EQ #8: How do you identify the key features of functions on graphs? MAFS.912.F-IF.2.4 EQ #9:How do you determine the domain and range of a piece wise function? MAFS.912.F-IF.2.4, MAFS.912.F-IF.1.2 EQ #10: How do functions transform? MAFS.912.F-BF.2.3 MAFS.912.A-APR.1.1: Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. MAFS.912.A-SSE.1.1 : Interpret expressions that represent a quantity in terms of its context. Interpret parts of an expression, such as terms, factors, and coefficients. MAFS.912.A-SSE.1.2: Use the structure of an expression to identify ways to rewrite it. MAFS.912.A-CED.1.3 Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. MAFS.912.A-REI.2.3 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. MAFS.912.F-IF.1.1 Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If ˆ is a function and š is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y= f(x). MAFS.912.F-IF.1.2 Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. MAFS.912.F-IF.2.4 For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. MAFS.912.F-IF.2.5 Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. MAFS.912.F-IF.3.7b Graph functions expressed symbolically and show key features of the graph by hand in simple cases and using technology for more complicated cases. b. Graph square root, cube root, MAFS.912.F-BF.1.1.b.c. Write a function that describes a relationship between two quantities. b. Combine standard function types using arithmetic operations. For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model. c. Compose functions. MAFS.912.F-BF.2.3 Identify the effect on the graph of replacing f(x) by f(x) + k, kf(x), f(kx), and f(x +k) for specific values of k (both positive and negative); find the value of & given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.
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Left Picture: Adding and subtracting two functions.
Middle Picture: Multiplying two functions using the box method.
Right Picture: Dividing two functions.
Identifying Graphs of Functions
Graphs represent functions as long as it passes the Vertical Line Test.
Graphs represent functions as long as it passes the Vertical Line Test.
In addition, graphs of functions can be formed using a table of x and y values.
Linear Functions: these functions include a slope and a y intercept. Slope is the rate of change or how steep the line will be graphed. A y-intercept is where the graph crosses the y axis.
X intercept: Where the graph crosses the x - axis.
Other Functions- Identify where the graph is crossing the y-axis and x - axis.
Linear Functions: these functions include a slope and a y intercept. Slope is the rate of change or how steep the line will be graphed. A y-intercept is where the graph crosses the y axis.
X intercept: Where the graph crosses the x - axis.
Other Functions- Identify where the graph is crossing the y-axis and x - axis.
Identifying Key Features on a Graph
1.When finding the increasing and decreasing intervals of a graph, you have to read the graph from left to right. Disregard the direction the end arrows point in.
2. Relative minimum: The lowest point on the graph
Relative maximum: The highest point on the graph
3. Finding the Domain: Where the function lives based on the x-axis
Finding the Range: Where the function lives based on the y-axis
1.When finding the increasing and decreasing intervals of a graph, you have to read the graph from left to right. Disregard the direction the end arrows point in.
2. Relative minimum: The lowest point on the graph
Relative maximum: The highest point on the graph
3. Finding the Domain: Where the function lives based on the x-axis
Finding the Range: Where the function lives based on the y-axis
Piecewise Functions
A piecewise function is a function made up of pieces. This type of function has intervals for its domain values. When evaluating a piecewise function, the given x value only makes one interval true. Once you find the interval the x value belongs to, then you use its corresponding function to plug that x value into.
Below is a link to an instructional video on piecewise functions.
www.youtube.com/watch?v=Vo9Y2X2wGbo
Piecewise Functions can form many different shapes. One shape is called a step function because linear lines form steps.
A piecewise function is a function made up of pieces. This type of function has intervals for its domain values. When evaluating a piecewise function, the given x value only makes one interval true. Once you find the interval the x value belongs to, then you use its corresponding function to plug that x value into.
Below is a link to an instructional video on piecewise functions.
www.youtube.com/watch?v=Vo9Y2X2wGbo
Piecewise Functions can form many different shapes. One shape is called a step function because linear lines form steps.
Function Transformations
Graphs change from the original function (aka parent function).
When the change is either added, subtracted, or multiplied to f(x), the function is changing on the y axis.
When the change is either added, subtracted, or multiplied on the x, then the function is changing on the x axis.
Graphs change from the original function (aka parent function).
When the change is either added, subtracted, or multiplied to f(x), the function is changing on the y axis.
When the change is either added, subtracted, or multiplied on the x, then the function is changing on the x axis.