Answer:
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) [tex]f(1)=0[/tex], [tex]f(-4)=2[/tex] , [tex]f(-1)=0[/tex]
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) [tex]g(0)=1[/tex], [tex]g(5)=3.5[/tex] , [tex]g(9)=1[/tex]
Step-by-step explanation:
Part 1) we have
[tex]f(x)=-\frac{2}{3}x-\frac{2}{3}[/tex] -----> For [tex]-4\leq x<-1[/tex]
[tex]f(x)=1-x^{2}[/tex] -----> For [tex]-1\leq x\leq 1[/tex]
[tex]f(x)=1[/tex] -----> For [tex]1 < x\leq 4[/tex]
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
[tex]f(x)=1-x^{2}[/tex]
substitute
[tex]f(1)=1-(1)^{2}=0[/tex]
a2) g(5)
we know that
For x=5
[tex]f(x)=-\frac{2}{3}x-\frac{2}{3}[/tex]
substitute
[tex]f(-4)=-\frac{2}{3}x-\frac{2}{3}=2[/tex]
a3) f(-1)
For x=-1
[tex]f(x)=1-x^{2}[/tex]
substitute
[tex]f(-1)=1-x^{2}=0[/tex]
Part 2) we have
[tex]g(x)=-(x+3)^{2}+4[/tex] -----> For [tex]3\leq x<0[/tex]
[tex]g(x)=(x+2)/2[/tex] -----> For [tex]0\leq x < 6[/tex]
[tex]g(x)=4/(x-5)[/tex] -----> For [tex]6 \leq x\leq 9[/tex]
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
[tex]g(x)=(x+2)/2[/tex]
substitute
[tex]g(0)=(0+2)/2=1[/tex]
a2) g(5)
we know that
For x=5
[tex]g(x)=(x+2)/2[/tex]
substitute
[tex]g(5)=(5+2)/2=3.5[/tex]
a3) g(9)
For x=9
[tex]g(x)=4/(x-5)[/tex]
substitute
[tex]g(9)=4/(9-5)=1[/tex]
