Question

Graph each absolute value function. State the domain, range, and y-intercept.

Answer 1

Answer:

i. D:All real numbers

ii.R:
`y\le-2`

iii. Y-int:
`b=-2.5`

Explanation:

The given function is


`y=-(1)/(2) |x-1|-2`

The domain of this function are the values of x that makes the function defined.

The absolute value function is defined for all real values.

The domain is all real numbers.

ii. The range refers to the values of y for which x is defined.


`y=-(1)/(2) |x-1|-2`

The vertex of this function is


`(1,-2)`

The function is reflected in the x-axis.

The vertex is therefore the maximum point on the graph of the function.

The range is therefore;


`y\le-2`

Or


`(-\infty,2]`

iii. To find the y-intercept, we substitute
`x=0` into the funtion.


`y=-(1)/(2) |0-1|-2`


`y=-(1)/(2) (1)-2`


`y=-2.5`

The y-intercept is
`b=-2.5`

The graph is shown in the attachment.