Answer:
Options (1) and (5)
Step-by-step explanation:
Expression that defines the function is,
[tex]f(x)=\frac{1}{2}x+\frac{3}{2}[/tex]
Option 1
[tex]f(-\frac{1}{2})=\frac{1}{2}(-\frac{1}{2})+\frac{3}{2}[/tex]
[tex]=-\frac{1}{4}+\frac{3}{2}[/tex]
[tex]=-\frac{1}{4}+1+\frac{1}{2}[/tex]
[tex]=1+\frac{1}{4}[/tex]
[tex]=1\frac{1}{4}[/tex]
So, [tex]f(-\frac{1}{2} )=-2[/tex] is false.
Option 2
f(0) = [tex]\frac{1}{2}(0)+\frac{3}{2}[/tex]
= [tex]\frac{3}{2}[/tex]
True.
Option 3
f(1) = [tex]\frac{1}{2}(1)+\frac{3}{2}[/tex]
= [tex]\frac{3+1}{2}[/tex]
= 2
Therefore, f(1) = -1 is false.
Option 4
[tex]f(2)=\frac{1}{2}(2)+\frac{3}{2}[/tex]
[tex]=1+1+\frac{1}{2}[/tex]
[tex]=2\frac{1}{2}[/tex]
Therefore, f(2) = 1 is false.
Option 5
f(4) [tex]=\frac{1}{2}(4)+\frac{3}{2}[/tex]
[tex]=2+\frac{3}{2}[/tex]
[tex]=\frac{4+3}{2}[/tex]
[tex]=\frac{7}{2}[/tex]
True.
Options (1) and (5) are the correct options.
