The function f is defined as follows fx x 5 if 4 lessthano

The function f is defined as follows. f(x) = {x + 5 if -4 lessthanorequalto x 1 Find the domain of the function. Locate any intercepts. Graph the function. Based on the graph, find the range. is f continuous on its domain? The domain of the function f is Locate any intercepts. Select the correct choice below and. if necessary, fill in the answer box to complete your choice. (Type an ordered pair. Use a comma to separate answers as needed.) There are no intercepts. Choose the correct graph below. The range of the function f is (Type your answer in interval notation.) Is f continuous on its domain? Select the correct choice below and. if necessary, fill in the answer box to complete your choice. No. f is discontinuous at x = (Use a comma to separate answers as needed.) Yes. f is continuous on its domain.

Solution

Its a piece wise function

Domain : all x values for which f(x) is defined :

[-4 , inf )

Intercept :

f(x) = x+5

( -5 , 0) and ( 0, 5)

f(x) = -x+3

( 3, 0) and ( 0 , 3)

However within the domain, intercepts are : ( 0,5) , ( 3, 0) and (0, 3)

Graph of function :

There is discontinuity at x=1

So, f(x) is not conitinous in its domain.

as f(x) = x+5 ---> f(1) = 6

f(x) = 9 for x =1

f(x) = -x +3 ----> f(1) = 2

Option B matches the desired graph as per f(x) given

Range of f(x) from graph : ( -inf , 9 ]