Consider the function f with the following properties: f is continuous everywhere except at r = -1 f(-3) = 1, ƒ(-2) = 0, ƒ(0) = -2 lim f(x) = +∞, lim f(x) = -o, lim f(x) = 2, lim [f(x) – (-x – 1)] = 0 x→-1- x→-1+ x→+∞ Intervals f" Conclusions (-00, –3) -3 0. (-3, –2) -2 (-2, –1) -1 DNE DNE (-1,0) 0. (0, +00)

Consider the function f with the following properties: f is continuous everywhere except at r = -1 f(-3) = 1, ƒ(-2) = 0, ƒ(0) = -2 lim f(x) = +∞, lim f(x) = -o, lim f(x) = 2, lim [f(x) – (-x – 1)] = 0 x→-1- x→-1+ x→+∞ Intervals f" Conclusions (-00, –3) -3 0. (-3, –2) -2 (-2, –1) -1 DNE DNE (-1,0) 0. (0, +00)

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter3: Functions

Section3.3: Rates Of Change And Behavior Of Graphs

Problem 2SE: If a functionfis increasing on (a,b) and decreasing on (b,c) , then what can be said about the local...

See similar textbooks

Similar questions

Determine if the statemment is true or false. If the statement is false, then correct it and make it true. If the function f increases on the interval -,x1 and decreases on the interval x1,, then fx1 is a local minimum value.
If f is continuous for all nonzero x and y, and f(0,0)=0, then lim f(x,y)=0 as (x,y) approaches (0,0). True or False
For the function f(x) (X^2-3 if -3 ≤x2 C) is f continuous at x=2? D) does lim f(x) exist at x->4^-? E) does lim exist f(x) exist at x->4^+?
Find an example of a function f : [−1,1] → R such that for A := [0,1], the restrictionf |A(x) → 0 as x → 0, but the limit of f(x) as x → 0 does not exist. Show why
a) f(a) exists b) f(x) is defined for 0<x<a c) f isn't continuous at x=a d)lim x-->a f(x) exists e)lim x-->a f(x)=f(a) which ones are true? could be up to four choices. explain.
(a)Verify the First Mean-Value Theorem for the function g(x)=x^3 +1 on the interval [1,2]. (b) By definition f'(x)= Lim h approaches 0 of {f(x+h)-f(x)/h}. Verify that f'(x)= secx tanx if f(x)= sec x.
Calculate if there exists lim x → 1f(x) and lim x → 4f(x) Is f continuous at x = 1? At x = 4?
Determine whether the statement " If f is continuous for all nonzero x and y, and f(0, 0) = 0, then (x, y) lim (0, 0) f(x, y) = 0. ", is true or false. If it is false, explain why or give an example that shows it is false.
Assume g is continuous from the right at x_0, g(x_0) is an interior point of the domain of f and f is continuous at g(x_0). Show that f of g= f(g(x)) is continuous from the right at x_0. What if we want to prove it is continuous from the left?
Consider the function f (x) given by f(x) = {kx, if x < 1; 0 if x = 1; 2k-kx if x > 1}, where k > 0 is a constant.a) For each of the three conditions for continuity, determine whether it is satisfied at point x = 1.b) Based on a), is f(x) continuous at x = 1? Does limx->1f(x) exsist? Is limitx->1f(x)=f(1)?
Consider a continuous function f(x)=2ex−1−2x. The graph of f is decreasing on which interval/s?