Download presentation

1
**3.5 Continuity & End Behavior**

2
Discontinuous – you cannot trace the graph of the function without lifting your pencil. (step and piecewise functions) Infinite discontinuity – the absolute value if f(x) becomes greater and greater as the graph approaches a given x-value. Jump discontinuity – the graph stops at a given value of the domain and then begins again at a different range value for the same value of the domain. Point discontinuity – when a value in the domain of the function is undefined, but the pieces of the graph match up Everywhere discontinuous – impossible to graph in the real number system

3
Continuity Test - A function is continuous at x = c if it satisfies the following conditions: 1. the function is defined at c; or f(c) exists 2. the function approaches the same y-value on the left and right sides of x = c 3. the y-value that the function approaches from each side is f(c).

4
**Ex 1 Determine whether the function is continuous at the given x-value.**

y = 3x2 + x – 7; x = 1

5
**Ex 2 Determine whether the function is continuous at the given x-value.**

6
**Ex 3 Determine whether the function is continuous at the given x-value.**

7
Continuity on an interval – a function f(x) is continuous on an interval if and only if it is continuous at each number x in the interval Critical points – points in the domain of the function where the function changes from increasing to decreasing or vice versa.

8
End behavior – describes what the y-values do as the absolute value of x becomes greater and greater. When x becomes greater and greater we say that x approaches infinity. (same notation is used for f(x) or y and using real numbers instead of infinity.)

9
**Ex 4 Describe the end behavior:**

f(x) = 5x3 g(x) = -5x3 + 4x2 – 2x + 4

Similar presentations

OK

1.5 Increasing/Decreasing; Max/min Tues Sept 16 Do Now Graph f(x) = x^2 - 9.

1.5 Increasing/Decreasing; Max/min Tues Sept 16 Do Now Graph f(x) = x^2 - 9.

© 2018 SlidePlayer.com Inc.

All rights reserved.

To ensure the functioning of the site, we use **cookies**. We share information about your activities on the site with our partners and Google partners: social networks and companies engaged in advertising and web analytics. For more information, see the Privacy Policy and Google Privacy & Terms.
Your consent to our cookies if you continue to use this website.

Ads by Google

Ppt on new technology in mobiles Ppt on non biodegradable waste management Download ppt on automatic street light control Ppt on global warming and acid rain Ppt on solar distillation system Ppt on event driven programming pdf Ppt on role of political parties in india Ppt on impact of french revolution Ppt on autism spectrum disorders Ppt on extinct birds and animals