Question

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

Answer 1

i) D: All real numbers

ii) R:
`y\le5`

iii) Y-int: b=2

Explanation:

i) The given absolute value function is

`y=-|x+3|+5`

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
`y=-|x+3|+5`

The function has vertex
`(-3,5)`.

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
`y\le 5` or
`(-\infty,5]`

iii) To find the y-intercept, put
`x=0` into the function.

`y=-|0+3|+5`

`y=-|3|+5`

`y=-3+5`

`y=2`

The y-intercept is (0,2) or
`b=2`

See attachment for graph.