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(a) Graph the function defined by $f(x)=\left\{\begin{aligned} 2 & \text { if } x<1 \\ 4 & \text { if } x=1 \\ 3-x & \text { if } x>1 \end{aligned}\right.$(b) Where is it discontinuous?(c) What kind of discontinuities does it have?

(a) THE ANSWER IS GRAPH (b) $x=1$(c) removable

Calculus 1 / AB

Chapter 2

An Introduction to Calculus

Section 3

Limits and Continuity

Derivatives

Missouri State University

Baylor University

Idaho State University

Lectures

04:40

In mathematics, a derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a moving object with respect to time is the object's velocity. The concept of a derivative developed as a way to measure the steepness of a curve; the concept was ultimately generalized and now "derivative" is often used to refer to the relationship between two variables, independent and dependent, and to various related notions, such as the differential.

30:01

In mathematics, the derivative of a function of a real variable measures the sensitivity to change of the function value (the rate of change of the value of the function). If the derivative of a function at a chosen input value equals a constant value, the function is said to be a constant function. In this case the derivative itself is the constant of the function, and is called the constant of integration.

01:10

The number of points at wh…

01:14

Given the function$$

01:09

04:19

(A) find the indicated val…

02:16

01:20

Let $f$ be a composite fun…

00:47

(a)graph the given functio…

02:32

01:00

The function $f(x)=\left\{…

01:47

Which function has a graph…

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