# Calculus

A function f(x) is said to have a removable discontinuity at x=a if:
1. f is either not defined or not continuous at x=a.
2. f(a) could either be defined or redefined so that the new function IS continuous at x=a.

--------------------------------------------------------------------------------
Let
Show that f(x) has a removable discontinuity at x=−7 and determine what value for f(−7) would make f(x) continuous at x=−7.
Must redefine f(−7)=_____________.
Now for fun, try to graph f(x). It's just a couple of parabolas!

1. 👍
2. 👎
3. 👁
1. f(x) is not given.

As an example, if f(x) is defined as follows:
f(x)=x² for x<0, and
f(x)=2x² for x>0.
Graph f(x) and you will find x=0 is undefined.
Since Lim f(x) x->0- equals Lim f(x) x->0+, we say that there is a removable discontinuity at x=0. The discontinuity can be removed by redefining f(x).

1. 👍
2. 👎
2. I'm sorry, I was having some problems posting the questions....

Again
Let

f(x)= mx-12 if x is less than -5
x^2 +5x - 7 if x is greater than -5
Show that f(x) has a removable discontinuity at x=−7 and determine what value for f(−7) would make f(x) continuous at x=−7.
Must redefine f(−7)=_____________.

1. 👍
2. 👎
3. OK I made a mistake... AGAIN fx is not equal to that sorry. I will repost this question.

1. 👍
2. 👎

## Similar Questions

Which of the following functions f has a removable discontinuity at a? If the discontinuity is removable, find a function g that agrees with f for x a and is continuous at a. (If the discontinuity is not removable, enter NONE.) 1.

2. ### math

Use a graph to determine whether the given function is continuous on its domain. HINT [See Example 1.] f(x) = x + 7 if x < 0 2x − 5 if x ≥ 0 1 continuous discontinuous If it is not continuous on its domain, list the points of

3. ### Calculus

Hi! My question is: Given that f is a function defined by f(x) = (2x - 2) / (x^2 +x - 2) a) For what values of x is f(x) discontinuous? b) At each point of discontinuity found in part a, determine whether f(x) has a limit and, if

4. ### precalculus

The function has a vertical asymptote of x=2 The function has a removable discontinuity of x=-2 The function has a horizontal asymptote of y= 0 No x intercept Y-intercept is (0,-0.5) End Behavior f(x) --> 0, x? -oo f(x) ? 0, x ?

1. ### calculus

give an example of a function that has: a) only one point of discontinuity b) exactly two ponts of discontinuity c) an infinite number of discontinuity give an example of a function that is: a) continuous at every point b)

2. ### Pre Cal

which of the following best describes the behavior of thre function f(x)=(x^2-2x)/(x^2-4) at the values not in its domain? a) one vertical asymptote, no removable discontinuities b) 2 vertical asymptotes c) two removable

3. ### Calculus

Let f(x)=(2x^2+5x-7)/(x-1) show that F(x) has a removable discontinuity at x=1 and determine what value for F(1) would make f(x) continuous at x=1 I'm not sure how to factor to solve for f(1)..

4. ### math

How do I find the continuity or discontinuity of a graphed function? I am stuck on this problem and cannot whatsoever get past it.

1. ### calculus

A function f(x) is said to have a removable discontinuity at x=a if: 1. f is either not defined or not continuous at x=a. 2. f(a) could either be defined or redefined so that the new function IS continuous at x=a. Let f(x)=

2. ### Math (Continuity)

Find the x-values (if any) at which f is not continuous. Which of the discontinuties are removable? f(x)=(x)/(x^2-4) I'm not sure how to do this problem but I know that it is not continnous at x=2?

3. ### Algebra 2

Find any points of discontinuity for the rational function. 1. (x + 6)(x + 2)(x + 8) y = _____________________ (x + 9)(x + 7) 2. x - 8 y = _____________________ x^2 + 6x - 7

4. ### ap calculus

Find the discontinuities of f(x)= ((x^2)+5x+6)/((x^2)-4)and categorize them as removable or non removable.