Question

Can someone please explain !!!

Answer 1

Part 1)

a) The graph in the attached figure

b) The domain of f(x) is the interval [-4,1] and the range is the interval [0,2]

c)
`f(1)=0`,
`f(-4)=2` ,
`f(-1)=0`

Part 2)

a) The graph in the attached figure

b) The domain of g(x) is the interval [-3,9] and the range of g(x) is the interval [1,13)

c)
`g(0)=1`,
`g(5)=3.5` ,
`g(9)=1`

Explanation:

Part 1) we have

`f(x)=-(2)/(3)x-(2)/(3)` -----> For
`-4\leq x<-1`

`f(x)=1-x^(2)` -----> For
`-1\leq x\leq 1`

`f(x)=1` -----> For
`1 < x\leq 4`

Part a) Graph the function

Using a graphing tool

Graph each function at the indicated intervals

see the attached figure

Part b) The domain of f(x) is the interval [-4,1]

All real numbers less than or equal to 1 and greater than or equal to -4

The range of f(x) is the interval [0,2]

All real numbers less than or equal to 2 and greater than or equal to 0

Part c) Determine

a1) f(1)

we know that

For x=1

`f(x)=1-x^(2)`

substitute

`f(1)=1-(1)^(2)=0`

a2) g(5)

we know that

For x=5

`f(x)=-(2)/(3)x-(2)/(3)`

substitute

`f(-4)=-(2)/(3)x-(2)/(3)=2`

a3) f(-1)

For x=-1

`f(x)=1-x^(2)`

substitute

`f(-1)=1-x^(2)=0`

Part 2) we have

`g(x)=-(x+3)^(2)+4` -----> For
`3\leq x<0`

`g(x)=(x+2)/2` -----> For
`0\leq x < 6`

`g(x)=4/(x-5)` -----> For
`6 \leq x\leq 9`

Part a) Graph the function

Using a graphing tool

Graph each function at the indicated intervals

see the attached figure

Part b) The domain of g(x) is the interval [-3,9]

All real numbers less than or equal to 9 and greater than or equal to -3

The range of f(x) is the interval [1,13)

All real numbers less than 13 and greater than or equal to 1

Part c) Determine

a1) g(0)

we know that

For x=0

`g(x)=(x+2)/2`

substitute

`g(0)=(0+2)/2=1`

a2) g(5)

we know that

For x=5

`g(x)=(x+2)/2`

substitute

`g(5)=(5+2)/2=3.5`

a3) g(9)

For x=9

`g(x)=4/(x-5)`

substitute

`g(9)=4/(9-5)=1`