Function Analysis Unit Test

Question

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Question
A state has a special inheritance tax on any money that you receive through inheritance. The tax rate depends on the amount of money you receive, as the following piecewise function shows.

f(x)=⎧⎩⎨⎪⎪0.3x if 0≤x≤20,0000.5x if 20,001 ≤x≤50,0000.1x if x≥50,001

When graphing the first part of the function, f(x)=0.3x
, what type of circles should be used for the endpoints?

(1 point)
Responses

Both ends should have open circles.
Both ends should have open circles.

The first point should be a closed circle and the last point should be an open circle.
The first point should be a closed circle and the last point should be an open circle.

The first point should be an open circle and the last point should be a closed circle.
The first point should be an open circle and the last point should be a closed circle.

Both ends should have closed circles.
Both ends should have closed circles.
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Answer 1

To determine what type of circles should be used for the endpoints of the function \( f(x) = 0.3x \) in the specified range \( 0 \leq x \leq 20,000 \):

1. The function \( f(x) = 0.3x \) is defined for \( x \) values inclusive of both endpoints, as indicated by \( 0 \leq x \leq 20,000 \).
2. This means that at \( x = 0 \) and \( x = 20,000 \), the values of the function are included in the function's output.

Since both endpoints are included in the range, we should use closed circles at both endpoints when graphing this part of the function.

Therefore, the correct response is: Both ends should have closed circles.