Piece wise function help?

Question

1. If Given H(x)=
√11-x ; x ≤ 2
(x-2)^2 ; 2 < x ≤ 5
2x-1 ; x > 5

Then what is h(2) ?
*Btw the root on the first one covers the -x too.

2. Given F(x)=
-3x ; x ≤ 2
(x-2)^2 ; 2 < x ≤ 5
2x-1 ; x > 5

Is the function discontinuous? If so where (think of its graph)?
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Please help as I am struggling with these..please do it step by step or explain because I have a hard time learning when it comes to math. Thank you in advance anybody who takes the time to answer, sorry I am desperate.

Answer 1

1)

 

To find h(2), you need to evaluate the square-root piece at x=2.  That is because it is in that domain.

 

 

2)

 

To determine whether the function is discontinuous, we need to evaluate the endpoints of each function.  If any piece of the function does not have the same value at their joining endpoints, then it is discontinuous.

 

Evaluate the first piece at x=2.

 

-3(2) = -6

 

 

Evaluate the middle piece at x=2.

 

(2 - 2)² = 0

 

 

Evaluate the middle piece at x=5.

 

(5 - 2)² = 9

 

 

Evaluate the last piece at x=5.

 

2(5) - 1 = 9

 

 

The first two pieces of the function do not have the same result at x=2.  Therefore, there is a discontinuity at x=2.  But it is continuous everywhere else.