Question

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

Answer 1

Answer:

I. D: $x\in R$

ii. R: $y\le0$

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

Step-by-step 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.