Question

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

Answer 1

i)D:
`x\in R`

ii)R:
`y\ge3`

iii) Y-int:(0,3)

Explanation:

i) The given absolute value function is;

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

has vertex at, (0,3) and opens upwards.

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

The range is
`y\ge3`

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

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

`f(0)=0+3`.

`f(0)=3`.

The y-intercept is (0,3)

See attachment for graph.

Answer 2

The domain is
`(-\infty,\infty)` and its range is
`[3,\infty).`

The y-intercept is (0,3).

Explanation:

Consider the parent function
`y=|x|.` Its domain is
`x\in (-\infty,\infty)` and its range is
`y\in [0,\infty).`

The graph of the function
`y=|x|+3` is obtained from the graph of parent function by translation 3 units up (see diagram). This translation doesn't change the domain and will change the range of the function, thus the domain is
`(-\infty,\infty)` and its range is
`[3,\infty).`

To find th y-intercept you have to find y at x=0:

`y=|0|+3=3.`

Hence, the y-intercept is (0,3).