Find the x-value at which f is not continuous. is the discontinuity removable?

Your teacher has decided to break down the problem into smaller chunks. The function f(x) will depend on what the x value is. If x is 2 or smaller, then f(x) = -6x as shown in the top row of the piecewise function. If x is larger than 2, then f(x) = x^2-7x+7.

So you'll put a -6 in the box for your image attachment to start off so you tell your teacher that f(x) = -6x when x = 2. Afterwards, plug x = 2 into f(x) = -6x to get f(2) = -12. Then plug x = 2 into f(x) = x^2-7x+7 to get -3. Since this value is not -12, this tells us we have a discontinuity at x = 2. This is a jump discontinuity as shown in the image attachment shown below. Note the closed circle at (2,-12) and the open circle at (2,-3). The open circle means "exclude this point from the graph".

step-by-step explanation:

first, eliminate the parenthesis:

3

x

+

2

−

4

x

second, group like terms:

3

x

−

4

x

+

2

third, combine like terms:

(

3

−

4

)

x

+

2

→

−

1

x

+

2

→

−

x

+

2