For what values of a and b would the function g(x) be continuous at x=-3 and have a point discontinuity at x=2

Question

g(x) = ax+3, x<-3

x^2-3x, -3 less than or equal to x < 2

bx-5, x>2

Answer 1

First, make sure I'm reading it correctly:

g(x) = ax+3, for x<-3

g(x) = ≤x^2-3x, for -3 ≤ to x < 2

g(x) =bx-5, for x>2

to find a: If g(x) is continuous at x = -3, you can simply plug that into each equation and solve for a:

-3a + 3 = (-3)² - 3*(-3)

-3a = 9 + 9 - 3 = 15

a = -5

Answer 2

Hi Ember,

The question is asking us to match up each of the function’s pieces with each other. So we want:

ax + 3 = x² - 3x when x = -3, which means we plug in x = -3 and get

-3a + 3 = (-3)² - 3(-3)

-3a + 3 = 9 + 9

a = -5

x² - 3x = bx - 5 when x = 2, so plug in x.= 2

(2)² - 3(2) = b(2) - 5

4 - 6 = 2b - 5

b = 1.5

Please let me know if I can be more helpful, thanks!

Joe