Question

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

Answer 1

i)D:
`x\in R`

ii)R:
`y\ge-3`

iii) Y-int:(0,-1)

Explanation:

i) The given absolute value function is;

`f(x)=|x+2|-3`.

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,

`f(x)=|x+2|-3`.

has vertex at, (-2,-3) and opens upwards.

This implies that, the minimum y-value is -3.

The range is
`y\ge-3`

iii) To find the y-intercept substitute x=0 in to the function.

`f(0)=|0+2|-3`.

`f(0)=|2|-3`.

`f(0)=2-3`.

`f(0)=-1`.

The y-intercept is (0,-1)

See attachment for graph.