Math - Continuity

Determine the constants a and b so that the function f is continuous on the entire real line:

f(x) = 2 , x=<-1
ax + b , -1<x<3
-2 , x>=3

could someone help me with this question please? thank you.

  1. 👍
  2. 👎
  3. 👁
  1. For continuity at x=-1, ax + b must equal 2 at x=-1
    Therefore -a + b = 2
    For continuity at x=3, ax+b must equal -2 there.
    Therefore 3a + b = -2

    Solve those two equations in two unknowns for a and b.
    4a = -4
    a = -1
    b = 2 + a = ?

    1. 👍
    2. 👎
  2. THANK YOU!!

    1. 👍
    2. 👎

Respond to this Question

First Name

Your Response

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. 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

  2. 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.

  3. CHEMISTRY HELP!

    Consider the following reactions and their equilibrium constants. (NO(g) + 0.5Br2(g) NOBr(g) Kp = 5.3 2NO(g) N2(g) + O2(g) Kp = 2.1 x 1030 Use these equations and their equilibrium constants to determine the equilibrium constant

  4. 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)=

  1. 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.

  2. math

    determine whether this relation is a function, state its domain and range, is it continuous or discrete. {(-3,0), (-1,1), (0,1), (4,5), (0,6)}

  3. 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

  4. Mathematics

    How do i solve the pair of simultaneous equations y=x^2-3x-12 and y=2x-16 and epxress y=x^2-3x-12 in the form y=(x-h^2)+k, where h and k are constants Hence determine the minimum value of the function y=x^2-3x-12 I have a few of

You can view more similar questions or ask a new question.