MATH(O) Limits and Continuity.

Slides:

Advertisements

Similar presentations

9.3 Rational Functions and Their Graphs

Advertisements

ACT Class Opener: om/coord_1213_f016.htm om/coord_1213_f016.htm

Limit & Derivative Problems Problem…Answer and Work…

3.7 Graphing Rational Functions Obj: graph rational functions with asymptotes and holes and evaluate limits of rational functions.

10.2: Infinite Limits. Infinite Limits When the limit of f(x) does not exist and f(x) goes to positive infinity or negative infinity, then we can call.

Section Continuity. continuous pt. discontinuity at x = 0 inf. discontinuity at x = 1 pt. discontinuity at x = 3 inf. discontinuity at x = -3 continuous.

Section 1.4 Continuity and One-sided Limits. Continuity – a function, f(x), is continuous at x = c only if the following 3 conditions are met: 1. is defined.

9.3 Rational Functions and Their Graphs Rational Function – A function that is written as, where P(x) and Q(x) are polynomial functions. The domain of.

Jeopardy Limits Limits with Trig Slope of a Curve Continuity Potpourri $100 $200 $300 $400 $500 $100 $200 $300 $400 $500.

Limits. a limit is the value that a function or sequence "approaches" as the input approaches some value.

Asymptotes Objective: -Be able to find vertical and horizontal asymptotes.

What is the symmetry? f(x)= x 3 –x.

6) 7) 8) 9) 10) 11) Go Over Quiz Review Remember to graph and plot all points, holes, and asymptotes.

Do Now: Explain what an asymptote is in your own words.

Limits Involving Infinity Section 2.2. ∞ Infinity Doesn’t represent a real number Describes the behavior of a function when the values in its domain or.

2.5 – Continuity A continuous function is one that can be plotted without the plot being broken. Is the graph of f(x) a continuous function on the interval.

A function, f, is continuous at a number, a, if 1) f(a) is defined 2) exists 3)

Informal Description f(x) is continuous at x=c if and only if there are no holes, jumps, skips or gaps in the graph of f(x) at c.

Review Limits When you see the words… This is what you think of doing…  f is continuous at x = a  Test each of the following 1.

Vertical and Horizontal Shifts of Graphs.  Identify the basic function with a graph as below:

8-3 The Reciprocal Function Family

Removable Discontinuities & Vertical Asymptotes

I can graph a rational function.

Lesson 3.6 (Continued) Graphing Exponential Functions : Graphing Exponential Functions.

Section Continuity 2.2.

Limits and Continuity Unit 1 Day 4.

1.3 – Continuity, End Behavior, and Limits. Ex. 1 Determine whether each function is continuous at the given x value(s). Justify using the continuity.

1.5 Infinite Limits. Find the limit as x approaches 2 from the left and right.

Point Value : 20 Time limit : 1 min #1. Point Value : 20 Time limit : 1 min #2.

Find f’(x) using the formal definition of a limit and proper limit notation.

Math – Exponential Functions

Calculus Section 2.5 Find infinite limits of functions Given the function f(x) = Find =  Note: The line x = 0 is a vertical asymptote.

REVIEW. A. All real numbers B. All real numbers, x ≠ -5 and x ≠ -2 C. All real numbers, x ≠ 2 D. All real numbers, x ≠ 5 and x ≠ 2.

Aim # 4.1 What are Exponential Functions?

4.4 Rational Functions II: Analyzing Graphs

2.5 Exploring Graphs of Rational Functions

Ch. 2 – Limits and Continuity

Warmup 3-7(1) For 1-4 below, describe the end behavior of the function. -12x4 + 9x2 - 17x3 + 20x x4 + 38x5 + 29x2 - 12x3 Left: as x -,

28 – The Slant Asymptote No Calculator

Functions JEOPARDY.

3.7 Graphs of Rational Functions

Ch. 2 – Limits and Continuity

4.4 Rational Functions II: Analyzing Graphs

Rational Functions and Their Graphs

4.4 Rational Functions Objectives:

Lesson 11.4 Limits at Infinity

26 – Limits and Continuity II – Day 2 No Calculator

3.5 Rational Functions II: Analyzing Graphs

Which is not an asymptote of the function

Rational Functions, Transformations

Limits involving infinity

Notes Over 9.3 Graphing a Rational Function (m < n)

3.5 Rational Functions II: Analyzing Graphs

F(x) = a b (x – h) + k.

A rational function is a function whose rule can be written as a ratio of two polynomials. The parent rational function is f(x) = . Its graph is a.

(4)² 16 3(5) – 2 = 13 3(4) – (1)² 12 – ● (3) – 2 9 – 2 = 7

Pre-Calculus Go over homework End behavior of a graph

Ex1 Which mapping represents a function? Explain

27 – Graphing Rational Functions No Calculator

3.5 Rational Functions II: Analyzing Graphs

Pre-Calculus 1.2 Kinds of Functions

I can graph a function with a table

EQ: What other functions can be made from

Which is not an asymptote of the function

Extra Sprinkling of Finals Review.

December 15 No starter today.

15 – Transformations of Functions Calculator Required

Continuity of Function at a Number

Exponential Functions and Their Graphs

Warm up honors algebra 2 3/1/19

Presentation transcript:

MATH(O) Limits and Continuity

1

Identify the horizontal asymptote(s) for: f(x) =-5 f(x) = 4 f(x) = -1 f(x) = 0 no horizontal asymptotes D

Does Not Exist

Based on the graph below, find:

Identify the horizontal asymptote(s) for: f(x) = -2 f(x) = -1 f(x) = 1/8 f(x) = 3 No horizontal asymptotes A

Find the value of a so that f(x) is continuous for all values of x.

Describe continuity of: Continuous Discontinuous non-removable at x = -6 Discontinuous removable at x = -6 Discontinuous non-removable at x = 0 C

Describe continuity of: Continuous Discontinuous removable at x = -4 Discontinuous removable at x = 4 Discontinuous non-removable at x = 4 Both B and C Both B and D B