Math Analysis Honors – MATH Sheets

M = Modeling A = Again T = Today’s Topic H = Homework

#0 Tuesday 9/2 ________________________________________M Welcome to Math Analysis! I am looking forward to a productive and successful year. A Sign up for class reminders one of two ways:

1) Text: @mrsfabell to (949)383-4519 in order to receive text messages2) Send a blank email to mrsfabell@mail.remind101.com

T Familiarize yourself with the procedures for this class. Stay eligible for the “contest”.H Be sure to print the worksheets.

#1 Tuesday 9/2_________________________________________

M 1. Find the slope of the line through

2. Find the equation of the line with slope 4 and containing the point .3. Graph the line from Ex. 2.

4. Find an equation for the line that contains the point and is parallel to the line .

5. Find an equation for the line that contains the point and is perpendicular to the line .

A Solve each equation algebraically: 1. 2. T Lines – Calculate and Interpret the Slope of a Line, Graph Lines, Finding Equations of Lines, Parallel and

Perpendicular LinesH Worksheet 1

#2 Wednesday 9/3______________________________________M A truck rental company rents a moving truck for one day by charging $29 plus $0.07 per mile. Write a linear

equation that relates the cost C, in dollars, of renting the truck to the number x of miles driven. What is the cost of renting the truck if the truck is driven 110 miles? 230 miles?

A Find the x- and y- intercepts of the graph of each function: 1. 2. T Linear Models – Work with Applications of Linear FunctionsH Worksheet 2

#3 Thursday 9/4_______________________________________

M 1. For the function f defined by , evaluate

(a) (b) (c) (d)

(e) (f) (g) (h) 2. Find the values of a function on a calculator

(a) (b)

A If and , what is the value of A?T Evaluating Functions, Using a graphing calculator, The Difference Quotient, Operations on FunctionsH Worksheet 3

#4 Friday 9/5________________________________________M Explain where the given functions are defined:

1. 2. 3. A Express the area A of a rectangle as a function of the length x if the length of the rectangle is twice its width.

Describe the domain of this function.T Domain of a FunctionH Worksheet 4

#5 Monday 9/8________________________________________

M Consider the function:

(a) Is the point on the graph of f?

(b) If , what is ? What point is on the graph?

(c) If , what is x? What point is on the graph?(d) What is the domain of f?(e) List the x-intercepts, if any, of the graph of f?(f) List the y-intercepts, if any, of the graph of f?

A 1. The intercepts of the equation are____________.2. True or False: A function can have more than one y-intercepts. Explain your reasoning.

T Properties of Graphs of Functions – x-intercepts, y-intercepts, H Worksheet 5

#6 Tuesday 9/9_____________________________________M NoneA NoneT Introduction to Functions TestH None

#7 Wednesday 9/10______________________________________M The figure at left shows the graph of a function f.

(a) At what number(s), if any, does f have a local maximum? (b) What are the local maxima? (c) At what number(s), if any, does f have a local minimum? (d) What are the local mimima? (e) List the interval(s) on which f is increasing. (f) List the interval(s) on which f is decreasing.

A Find the domain of .T Using a graph to determine where a function is increasing, decreasing and constant and to find Local Maxima and

Local Minima H Worksheet 6

#8 Thursday 9/11__________________________________________

M Use a graphing utility to graph for . Determine the point at which has a local maximum and where f has a local minimum. Determine where f is increasing and where it is decreasing.

A Evaluate for .

T Using a graphing calculator to determine where a function is increasing, decreasing and constant and to find Local Maxima and Local Minima

H Worksheet 7

#9 Friday 9/12_________________________________________M Graph the following functions

A Graph the following functions: 1. 2. 3. T Evaluating and Graphing Piecewise-Defined Functions H Worksheet 8

#10 Monday 9/15_______________________________________

M Exploration 1: Graph

Exploration 2: Graph

Exploration 3: Graph

Exploration 4: Graph

A Find the equation of the line perpendicular to the line and containing the point . Graph both lines.T Library of Functions: Quadratic, Absolute Value, Square Root, Cubic; Transformations H Worksheet 9

#11 Tuesday 9/16____________________________________M

Use the graph of f as the first step toward graphing each of the following functions:

(a) (b) (c)

(d) (e) (f)

A Given that g is a linear function with slope of and , write the equation that defines g.T Graphing Techniques: TransformationsH Worksheet 10

#12 Wednesday 9/17_____________________________________M None

A Find the x- and y- intercepts of the graph of each function: 1. 2. T Functions and Their Graphs Test H Worksheet 11

#13 Thursday 9/18________________________________________

M Graph: 1) 2) Identify the vertex and axis of symmetry.

Change the quadratic function from standard form to transformation (vertex) form: . Identify the vertex and axis of symmetry.

A Solve the quadratic equation by completing the square: T Quadratic Function; Graphing a Quadratic Function in Transformation (Vertex) FormH Worksheet 12

#14 Friday 9/19________________________________

M Ex. 1 Given , find the x-coordinate of the vertex by completing the square and converting the standard form equation into vertex form.

Ex. 2 Locate the vertex and axis of symmetry of the parabola defined by . Graph

.

Ex. 3 Graph . Determine where f is increasing and where it is decreasing.

A Given , list the transformations that occur in order to change into , if

.T Graph a Quadratic Function in Standard Form using its Vertex and Axis of SymmetryH Worksheet 13