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
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.
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.
Both ends should have closed circles.
Both ends should have closed circles.
Both ends should have open circles.
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
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.
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.
Both ends should have closed circles.
Both ends should have closed circles.
Both ends should have open circles.
Answers
GPT-4o mini
To determine the type of circles to use for the endpoints of the function \( f(x) = 0.3x \) for the interval \( 0 \leq x \leq 20,000 \), we need to look at the endpoints and whether they are included in the function.
The expression \( 0 \leq x \leq 20,000 \) indicates that the first point (at \( x = 0 \)) is included (closed circle) and the last point (at \( x = 20,000 \)) is also included (closed circle).
Therefore, you should use closed circles at both endpoints.
The correct response is:
**Both ends should have closed circles.**
The expression \( 0 \leq x \leq 20,000 \) indicates that the first point (at \( x = 0 \)) is included (closed circle) and the last point (at \( x = 20,000 \)) is also included (closed circle).
Therefore, you should use closed circles at both endpoints.
The correct response is:
**Both ends should have closed circles.**