Answer:
i) D:[tex]x\in R[/tex]
ii) R:[tex]y\le5[/tex]
iii)[tex]b=4.33[/tex]
Step-by-step explanation:
i) The given function is
[tex]y=-\frac{1}{3}|x-2|+5[/tex]
The function is defined for all real values of x.
The domain is all real numbers.
ii) The range is all values of y that makes x defined.
The given function is [tex]y=-\frac{1}{3}|x-2|+5[/tex]
This function has vertex [tex](2,5)[/tex] and it is reflected in the x-axis.
This means that, the vertex is the maximum point and the maximum y-value is 5.
The range is [tex]y\le5[/tex] or [tex](-\infty,5][/tex]
iii) To find the y-intercept. we subsitute [tex]x=0[/tex] into the function.
[tex]y=-\frac{1}{3}|0-2|+5[/tex]
[tex]y=-\frac{1}{3}|-2|+5[/tex]
[tex]y=-\frac{1}{3}(2)+5[/tex]
[tex]y=4.33[/tex]
The y-intercept is (0,4.33) or b=4.33
See attachment for graph
