# Q1W8 Algebra Teacher Carol Barnes Algebra 7th/8th Q1W8 Oct. 4-8 Unit 3 Introduction to Functions
Standard(s) Taught

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.A-REI.4.10  Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line).

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 f is a function and x 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-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 k 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.

Learning Targets and Learning Criteria
• choose and analyze inputs (and outputs) that make sense based on the problem.
• evaluate a function for a given domain value.

• determine what the domain for a function should be and create a graph that displays it.
• explain why the function for a given context has a continuous or discrete domain or range.
• explain why numbers might be excluded from a domain.
• connect a function to the context it represents using quantities.
• find the key features of the graphs and tables of a function.
• interpret the meaning of an ordered pair.
• determine if negative inputs and/or outputs make sense in the problem.
• identify and explain the x and y intercept and what it means in a problem situation.
• explain that a function can have only one y-intercept but can have more than one x-intercept.
• define whether the function is increasing and decreasing from a table, graph, or problem situation.
• define and identify the relative minimums and maximums on a table, graph, or problem situation.
• explain why f(x) + k translates the original graph of f(x) up k units and why f(x)-k translates the graph down k units.
• explain why f(x + k) translates the original graph to the left k units and why f(x – k) translates the graph to the right k units.
• identify the zeros from a graph of a polynomial
• identify the zeros of factored polynomials.
Classroom Activities

Monday/Tuesday:

Bellringer:  Find the value of the function f(x) = 4x-2  for x = 3.5  AND  graph f(x)=x squared, then graph g(x)=x squared + 2.  Notice the shift in the new parabola that is graphed for g(x) is 2 above the graph for f(x).  Adding two to the equation for f(x) cause the graph to shift two above the original graph.

Whole Group:  ISN page 12 Domain and Range of Functions expressed with inequalities or equations. Domain and Range Notes for Functions.  Do problems 1 – 6 with class.

Small Group: Students do problems 7-14 with a shoulder partner.  Check answers to key then insert as page 15 into ISN.

Independent:  HW page #1  Domain and Range HW 1

Key for Domain and Range Notes  Domain and Range Notes Key

Wednesday:

Bell Ringer:  Substitute x = 4 into f(x) =  x squared -5x +2;  Find the maximum & minimum on the graph on the board.

Whole group:  Answer questions on homework (domain & range).  Find the absolute maximum and minimum of the function f(x) on the board.  Find the relative maximums and minimums on the graph on the board.  (Refer to Khan Academy Videos under Algebra, then functions – maximum and minimum points).  Find the “zeros” or x-intercepts on the graphs projected on the board.  On coordinate plane graph on whiteboard, observe a vertical shift in the graph of a function f(x) = x squared.

Small group: With a partner, find the vertical or horizontal shift in the graphs projected on the board.

Independent:  Khan Academy-Absolute Maxima and Minima, and Relative Maxima and Minima

Thursday/Friday:

Bellringer:  On paper provided with a parent graph of f(x) = x squared, graph the shift of g(x) = f(x)-3.  A student will draw the graph on the board.

Whole Group:  ISN – Page 16  Take notes to explain that a function [we’ll call it h(x)] with a horizontal shift (left or right) is shown like this:  h(x) = f(x – horizontal shift), so if a graph is to show a negative shift of 4 to the left (-4), in the format above it looks like this: h(x) = f(x – – 4) Notice the double negative in front of the four.  The double negative makes the four positive, so it ends up looking like this h(x) = f(x + 4),  and represents a shift of the graph horizontally to the left 4 units.  I you want the graph to shift to the right 3 units, it looks like this:  h(x) = f(x – 3).  These shifts will be drawn on the board and copied with colored pencil onto the paper provided for the bell ringer above.

Small Group:  ISN page 17 is a half page insert of a graph of a function.  Partners will find domain, range, x-intercept, y-intercept, maximum, minimum, increase, and decrease on the graph.

Independent:  Khan Academy –  Positive and Negative Intervals, and Increasing and Decreasing Intervals.

Assignments Due

Domain and Range HW 1 page (printed page)

Khan Academy:  Absolute Maxima and Minima, Relative Maxima and Minima, Positive and Negative Intervals, and Increasing and Decreasing Intervals.

Functions Real World Graphs HW 2  11 problems (printed page)

IXL  Q.16  to 80%