Question

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

Answer 1

i) D:
`x\in R`

ii) R:
`y\le5`

iii)
`b=4.33`

Explanation:

i) The given function is

`y=-(1)/(3)|x-2|+5`

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
`y=-(1)/(3)|x-2|+5`

This function has vertex
`(2,5)` 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
`y\le5` or
`(-\infty,5]`

iii) To find the y-intercept. we subsitute
`x=0` into the function.

`y=-(1)/(3)|0-2|+5`

`y=-(1)/(3)|-2|+5`

`y=-(1)/(3)(2)+5`

`y=4.33`

The y-intercept is (0,4.33) or b=4.33

See attachment for graph