Question

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

Answer 1

Answer:

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

The y-intercept is (0,3).

Step-by-step 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).

Answer 2

Answer:

i)D:$x\in R$

ii)R: $y\ge3$

iii) Y-int:(0,3)

Step-by-step 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.