Answer:
i)D:[tex]x\in R[/tex]
ii)R: [tex]y\ge-3[/tex]
iii) Y-int:(0,-1)
Step-by-step explanation:
i) The given absolute value function is;
[tex]f(x)=|x+2|-3[/tex].
The absolute value function is defined for all real values of x.
The domain is all real numbers.
ii) The range is all y-values that will make x defined.
The given function,
[tex]f(x)=|x+2|-3[/tex].
has vertex at, (-2,-3) and opens upwards.
This implies that, the minimum y-value is -3.
The range is [tex]y\ge-3[/tex]
iii) To find the y-intercept substitute x=0 in to the function.
[tex]f(0)=|0+2|-3[/tex].
[tex]f(0)=|2|-3[/tex].
[tex]f(0)=2-3[/tex].
[tex]f(0)=-1[/tex].
The y-intercept is (0,-1)
See attachment for graph.
