Question

Help with limits?
Find a and b

f(x)= {2, x<1
{ax+b, -13

Answer 1

the less than sign for x<1 is actually a less than or equal to and the greater than sign for x>3 is actually a greater than or equal to

Answer 2

in the back of my book the answer says a=-1 and b=1 though..

Answer 3

Is x<1 or -1?

Answer 4

is the function, though piecewise, supposed to be continuous?

Answer 5

x is less than or equal to -1 and x is greater than or equal to 3

Answer 6

oh ok that's why it didnt work

Answer 7

I was using 1

Answer 8

hmmm \(\large f(x) =
\begin{cases}
2, &x \le -1\\
ax+b, & -1 < x < 3\\
-2, & x \ge 3
\end{cases}\) ?

Answer 9

so 2=a(-1)+b

2=-a+b

2+a=b

so

-2=a(3)+(2+a)
-4= 3a+a
-4=4a
a=-1

Now it works

Answer 10

2+-1= 1=b

Answer 11

Now does it make sense?

Answer 12

hmmm, I am assuming all that's to make it continuous... hmm

Answer 13

Yes it's a continuous extension type of thing

Answer 14

I don't understand how you knew what to do

Answer 15

like how did you know to set 2 to ax+b?

Answer 16

Well, the point is to make the function continuous at X=-1 and 3. So you want to find the values of a and b that will complete the function and "unite" the 3 smaller functions.

Answer 17

wait so the -1 and the -3 are pretty much what x is approaching?

Answer 18

Exactly

Answer 19

I assume is \(f(x) =
\begin{cases}
2, &x \le -1\\
ax+b, & -1 < x < 3\\
-2, & x \ge 3
\end{cases}\)

thus, ax+b is really the equation a line, a line that goes from that point ON THE UPPER-LEFT to that other point ON THE LOWER-RIGHT

Answer 20

anyhow, once you have 2 points for it, you can pretty much get the equation for the line, using the point-slope equation

Answer 21

you don't need to use the point-slope equation.. but thanks

Answer 22

The point of this is to be able to solve the problem algebraically @jdoe0001, without the use of graphs.

Answer 23

right, I saw that :)

Answer 24

Awks I didn't see you were still on the problem - just ignore the message I sent. How did you get b?

Answer 25

@jdoe0001 @TheDoctorRules answer her, please

Answer 26

@dan815

Answer 27

I'm with jdoe0002 (XD) . I'm stick with slope of the line. However, your problem need the condition of "f(x) is continuous at the interval (-1,3)
from then you can find a =-1 , b =1