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Federal Income Taxes and Piecewise Functions LC)

The graph of a piecewise function is shown.

What is the range of the function?

(−∞, −2) ∪ [−1, 1] ∪ (2, ∞)
(−∞, −2] ∪ (−1, 1) ∪ [2, ∞)
(−∞, ∞)
[−∞, ∞]

Federal Income Taxes and Piecewise Functions LC) The graph of a piecewise function-example-1
User Jendrik
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1 Answer

2 votes

Answer:

2nd choice

(−∞, −2] ∪ (−1, 1) ∪ [2, ∞)

Explanation:

The range of a function is the set of y-coordinates.

Look at the graph starting from the left side.

The graph keeps going down to the left, so the minimum value if negative infinity, -∞.

From there, it goes up to a y-value of -2 with a closed dot, so -2 is included. That gives you this part of the range: (−∞, −2]

There are no y-values from y = -2 to y = -1, and -1 has an open dot.

There are y-values from just above -1 to 1, again with an open dot. That gives you the interval (−1, 1).

At y = 2 with a closed dot, the y-values start again and go up forever to positive infinity producing the interval [2, ∞).

The range is the union of the three intervals above.

Answer:

2nd choice

(−∞, −2] ∪ (−1, 1) ∪ [2, ∞)

User Don B
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