TOPIC 1 Preparing for Calculus A) Exponential and Logarithmic Functions B) Properties of Logarithms C) Exponential and Logarithmic Equations

8/21/2018 Discussion and Notes Interactive Practice and Examples Classwork pg. 41-48 including discussion of concepts, definition and properties. Domain and range of exponential and logarithmic functions. Graph of exponential and logarithmic functions, brief explanation about horizontal, vertical and oblique asymptotes. Solving exponential and logarithmic equations. Relation between exponential and logarithmic functions.

8/22/2018 Notes, Interactive Practice and Examples including properties of logarithms and solving logarithmic equations. Properties of Logarithms and examples from pgs. 49-50 Classwork worksheet (Resume # 12) 8/23/2018 Practice worksheet 12-30.

8/24/2018 Complete practice worksheet online 30-40

TOPIC 2 Functions A) Symmetry (Respect to the origin, the x-axis or the y-axis. B) Continuity (Continue or discontinue) C) Monotony (Increasing, decreasing) D) Maxima and Minima (relative and Absolute)

8/27/2018 Check the last two questions of lesson 1.1 practice (graphs). Discuss concepts of continuity, symmetry, monotony, relative and absolute maxima and minima. HW: Study for Lesson 1.1 Test on Tuesday 8/28/2018

A function f(x) is discontinuous at those values of x where Discontinuity A function f(x) is discontinuous at those values of x where - The function is undefined. - The function has holes. - The function has vertical asymptotes. - The function is a piecewise function. Symmetry - If f(x) = - f(x), then f(x) is symmetric about the x-axis. - If f(x) = f(-x), then f(x) is symmetric about the y-axis, and the function is even. - If f(-x) = - f(x), then f(x) is symmetric about the origin and the function is odd. Monotony - A function is increasing in an open interval I, if for any two values 𝒙 𝟏 , 𝒙 𝟐 in I and 𝒙 𝟏 < 𝒙 𝟐 , f( 𝒙 𝟏 ) < f( 𝒙 𝟐 ) - A function is decreasing in an open interval I, if for any two values 𝒙 𝟏 , 𝒙 𝟐 in I and 𝒙 𝟏 < 𝒙 𝟐 , f( 𝒙 𝟏 ) > f( 𝒙 𝟐 ) - A function is constant in an open interval I, if for any two values 𝒙 𝟏 , 𝒙 𝟐 in I and 𝒙 𝟏 < 𝒙 𝟐 , f( 𝒙 𝟏 ) = f( 𝒙 𝟐 )

8/28/2018 TEST Logarithmic and Exponential functions

8/29/2018 Relative extrema (Maximum or minimum). Relative or local extremum occurs in an open interval. Absolute extrema (Maximum or minimum). Absolute extremum occurs on a closed interval. The absolute maximum or minimum requires you to check the endpoints of the interval to see if the y-values are greater than or less than the extrema found within the interval. -Critical numbers occur where the function changes from decreasing to increasing and vice-versa. - Inflection points those points where the concavity of the function change. However, inflection may change at one of the undefined values, but if it is not in the domain, it is not part of the graph, cannot be an inflection point. -If f is continuous on a closed interval [a,b], then f has both a minimum and a maximum on the interval.

A local maximum (or minimum) is a point (c,f(c )) such that f© is the greatest (or the least) value of the function in some interval around c. A local minimum or maximum is also called a relative minimum or maximum. The global minimum (or maximum) is the point where f(x) assumes its least (or greatest) value in the domain considered. The global minimum or maximum is also called the absolute minimum or maximum. If the domain is a closed interval (an interval that includes its endpoints), then a continuous function will always have global minimum and maximum points, possibly at one of the endpoints. Critical points are points where the slope of the tangent is zero or is undefined. All extrema – that is, all minima and maxima- happen either at endpoints or at critical points. 01 - Continuity.pdf 01 - Extrema, Increase and Decrease.pdf

8/31/2018 Explain the Continuity worksheet 9/4/2018 -Continue explaining the Continuity worksheet 9/5/2018 - WORKSHEET Classwork 01 - Extrema, Increase and Decrease.pdf 9/6/2018 -KHAN ACADEMY VIDEO OF EXTREMA - WORKSHEET Classwork 01 - Extrema, Increase and Decrease.pdf

-KHAN ACADEMY VIDEO OF CONTINUITY - WORKSHEET Classwork 01 - Extrema, Increase and Decrease.pdf 9/7/2018

TOPIC 3 TRIGONOMETRIC FUNCTIONS A) Unit Circle. B) Periodic Functions. C) Fundamental trigonometric functions D) Verifying trigonometric identities 9/11/2018 (9/10/2018 TEACHER PLANNING DAY)

9/11/2018

9/17/2018 Checking Test

9/13/2018

9/13/2018

TOPIC 4 Limits & Continuity A) Finding Limits graphically and Numerically B) Evaluating Limits Analytically C) Limits Involving Infinity D) Continuity 917/

9/13/2018

9/17/2018

2.1 Evaluating limits by substitution.docx

8/25/2018

9/26/2018

9/27/2018 Resume Question 6

9/27/2018

10/2/2018

10/3/2018

10/5/2018

10/11/2018 Topics to study for the test

10/11/2018 Topics to study for the test

10/11/2018 Topics to study for the test

10/11/2018 Topics to study for the test

10/11/2018 Topics to study for the test

10/11/2018 Topics to study for the test