calculus

posted by .

Let f be defined as follows:
h(x)=

-x-3 for x greater than or equal to 1

ax+b for -2<x<1

x(squared) for x less than or equal to -2

Find the values of "a" and "b" that make h(x) continous.

I'm a bit stumped on how to go about solving this one. Help would be greatly appreciated. :)

• calculus -

look at the transition points, they should be the same.

when x = 1
h(x) = -x - 3 = -1-3 = -4
h(1) = a + b
so a+b = -4

h(-2) for ax+b = -2a+b
h(-2) for x^2 = 4
so -2a + b = 4

a+b = -4
-2a +b = 4
subtract:
3a = -8
a = -8/3,
back in a+b= -4
-8/3+b = 4
b = 20/3

a = -8/3 , b = 20/3

Similar Questions

1. math

sketch the feasible region for this system of the inqualities and find the coordinates of each vertex:y greater than or equal to 1;x less than or equal to 2; -1x+2y less than or equal to 6;1x+2y greater than or equal to 2
2. Calculus

Consider the function f(x)=6x-cos(x)+5 on the interval 0 is less than or equal to x, and x is less than or equal to 1. The Intermediate Value Theorem guarantees that there is a value c such that f(c)=k for which values of c and k?
3. calculus

Consider the function f(x)=65x−cos(x)+2 on the interval 0 less than or equal to x less than or equal to 1. The Intermediate Value Theorem guarantees that there is a value c such that f(c)=k for which values of c and k?
4. Calculus c

Let f be a twice-differentiable function defined on the interval -1.2 less than or equal to x less than or equal to 3.2 with f(1)=2. The graph of f', the derivative of f, is shown on the right. The graph of f' crosses the x-axis at …
5. Calculus

Let f be a twice-differentiable function defined on the interval -1.2 less than or equal to x less than or equal to 3.2 with f(1)=2. The graph of f', the derivative of f, is shown on the right. The graph of f' crosses the x-axis at …
6. math/calculus

The function f is defined as follows: f(x)={x+6 if -5 less than or equal to x<1 f(x)={9 if x=1 f(x)={-x+5 if x>1 a. find the domain b. locate any intercepts, if any
7. math

State the null hypothesis, Ho, and the alternative hypothesis, Ha, that would be used to test the following statements. (a) The linear correlation coefficient is positive. Ho: ñ ---Select--- not equal to equal to greater than less …
8. Math

Hi everyone, my name is Emerson. I was wondering if anybody could help me on a test. I'm stuck on some, but I think I know some others. Thank you! 1. Translate the phrase "nine more than two times a number" in to an algebraic expression. …
9. math

7. The tennis team is selling key chains as a fundraiser. If its goal is to raise is at least 180, how many key chains must it sell at \$2.25 each to meet that goal?
10. Algebra 2 A

What is the minimum value for z=3x-1/2y over the feasibility region defined by the constraints?

More Similar Questions