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lubasha [3.4K]
3 years ago
11

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

Mathematics
1 answer:
Inessa05 [86]3 years ago
3 0
Answer:

i. D:All real numbers

ii.R:y\le-2

iii. Y-int: b=-2.5

Step-by-step explanation:

The given function is

y=-\frac{1}{2} |x-1|-2

The domain of this function are the values of x that makes the function defined.

The absolute value function is defined for all real values.

The domain is all real numbers.

ii. The range refers to the values of y for which x is defined.

y=-\frac{1}{2} |x-1|-2

The vertex of this function is

(1,-2)

The function is reflected in the x-axis.

The vertex is therefore the maximum point on the graph of the function.

The range is therefore;

y\le-2

Or

(-\infty,2]

iii. To find the y-intercept, we substitute x=0 into the funtion.

y=-\frac{1}{2} |0-1|-2

y=-\frac{1}{2} (1)-2

y=-2.5

The y-intercept is b=-2.5

The graph is shown in the attachment.

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