# calculus

find the constants a and b so the function is continuous on a real line
piecewise function:
f(x)={5, if x<= -2; ax+b, if -2<x<3; -5, if x>=3

I know the limit x-->2- is 5 and limit x-->3+ is -5. I don't know how to find the constants

1. 👍
2. 👎
3. 👁
1. i have a=-2 and b=1

1. 👍
2. 👎
2. Forget about limits for a while and just consider the simple facts:
f(x) = 5 starts at -2 and goes to the left
then
f(x) = -5 starts at 3 and goes to the right.
Those two lines are "linked" by a straight line
from (-2,5) to (3,-5)
Let's just find that line .....
slope = -10/5 = -2
so (y-5) = -2(x+2)
y-5 = -2x - 4
y = -2x + 1
comparing with y = ax + b
a = -2 , b = 1

you had that, good job

1. 👍
2. 👎

## Similar Questions

1. ### calc urgent

Note that f is continuous on (−∞, 6) and (6, ∞). For the function to be continuous on (−∞, ∞), we need to ensure that as x approaches 6, the left and right limits match. First we find the left limit. lim x→6− f(x)

2. ### calculus

Find the constant a such that the function is continuous on the entire real line g(x)=x^2-a^2/x-a if x doesn't equal a 6 if x=a

3. ### math

Solve for the constants a and b that make the piecewise function continuous for all real numbers. f(x)= 4-2x-x^2, x1

4. ### 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

1. ### Functions - math

The function f is such that f(x) = 2x + 3 for x ≥ 0. The function g is such that g(x)= ax^2 + b for x ≤ q, where a, b and q are constants. The function fg is such that fg(x)= 6x^2 − 21 for x ≤ q. i)Find the values of a

2. ### Calculus

Explain, using the theorems, why the function is continuous at every number in its domain. F(x)= 2x^2-x-3 / x^2 +9 A) F(x) is a polynomial, so it is continuous at every number in its domain. B) F(x) is a rational function, so it

3. ### 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.

4. ### Calculus

If f(x) is a continuous function defined for all real numbers, f(-1)=1, f(-5)=-10, and f(x)=0 for one and only one value of x, then which of the following could be that x value? a) -6 b) -5 c) -4 d) 0

1. ### MATH

A continuous function, f, has domain all real numbers. If f(-1) = 5 and f(1) = -5, explain why f must have at least one zero in the interval [-1, 1].

2. ### Continuity Calculus Help

Find the value of constants c and d that make the function below continuous at x = 4. f(x) = x2 − 3x x < 4 c x = 4 d + x x > 4 c = d = 8 I got d=8, but finding c is giving me trouble.

3. ### 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)=

4. ### Calculus

Find the constants a and b such that the function is continuous on the entire line f(x){7, x is less than or equal to -3 ax+b, -3 is less than x is greater than 4 -7, x is less than or equal to 4