Answer:
i) D: All real numbers
ii) R: [tex]y\ge2[/tex]
iii) Y-int: b=2.25
Step-by-step explanation:
i) The given absolute value function is
[tex]y=\frac{1}{4}|x+1|+2[/tex]
The domain is all values of x that makes the function defined.
The absolute value function is defined for all values of x.
The domain is all real numbers.
ii) The given function is [tex]y=\frac{1}{4}|x+1|+2[/tex]
The function has vertex [tex](-1,2)[/tex].
Since [tex]a=\frac{1}{4}[/tex] is positive
This means the vertex is the minimum point on the graph of the function.
The minimum y-value is 2.
The range is therefore [tex]y\ge 2[/tex] or [tex][2,+\infty)[/tex]
iii) To find the y-intercept, put [tex]x=0[/tex] into the function.
[tex]y=\frac{1}{4}|0+1|+2[/tex]
[tex]y=\frac{1}{4}|1|+2[/tex]
[tex]y=\frac{1}{4}+2[/tex]
[tex]y=2.25[/tex]
The y-intercept is (0,2.25) or [tex]b=2.25[/tex]
See attachment for graph.
