Question

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

Answer 1

Answer:

i)D:$x\in R$

ii)R: $y\ge-3$

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

Step-by-step 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.