Question

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

Answer 1

Answer:

i) D: All real numbers

ii) R: $y\le5$

iii) Y-int: b=2

Step-by-step explanation:

i) The given absolute value function is

$y=-|x+3|+5$

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

The absolute value function is defined for all values of x.

The domain is all real numbers.

ii) The given function is $y=-|x+3|+5$

The function has vertex $(-3,5)$.

The function is reflected in the x-axis.

This means the vertex is the maximum point on the graph of the function.

The maximum y-value is 5.

The range is therefore $y\le 5$ or $(-\infty,5]$

iii) To find the y-intercept, put $x=0$ into the function.

$y=-|0+3|+5$

$y=-|3|+5$

$y=-3+5$

$y=2$

The y-intercept is (0,2) or $b=2$

See attachment for graph.