Answer:
i) D: All real numbers
ii) R: [tex]y\le5[/tex]
iii) Y-int: b=2
Step-by-step explanation:
i) The given absolute value function is
[tex]y=-|x+3|+5[/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=-|x+3|+5[/tex]
The function has vertex [tex](-3,5)[/tex].
The function is reflected in the x-axis.
This means the vertex is the maximum point on the graph of the function.
The maximum y-value is 5.
The range is therefore [tex]y\le 5[/tex] or [tex](-\infty,5][/tex]
iii) To find the y-intercept, put [tex]x=0[/tex] into the function.
[tex]y=-|0+3|+5[/tex]
[tex]y=-|3|+5[/tex]
[tex]y=-3+5[/tex]
[tex]y=2[/tex]
The y-intercept is (0,2) or [tex]b=2[/tex]
See attachment for graph.
