Question

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

Answer 1

I. D:
`x\in R`

ii. R:
`y\le0`

iii. Y-int:
`b=-6`

Explanation:

i) The given absolute value function is

`y=-3|x+2|`

The domain is all values of x that will make the function defined.

The absolute value function is defined for all real numbers.

The domain is all real numbers.

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

The given absolute value function is

`y=-3|x+2|`

This function has the vertex at
`(-2,0)` and it is reflected in the x-axis therefore the vertex is the maximum point on the graph.

The y-value of the vertex is the maximum value on the graph.

Hence the range is
`y\le0`

iii) To find the y-intercept, we put x=0, into the function to get;

`y=-3|0+2|`

`y=-3|2|`

`y=-3(2)`

`y=-6`

The y-intercept is
`b=-6` or (0,-6)

See graph in attachment.