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.
Both ends should have closed circles.
Both ends should have closed circles.
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.
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.
Both ends should have closed circles.
Both ends should have closed circles.
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.
Answers
GPT-4o mini
To determine the correct type of circles to use for the endpoints of the function \( f(x) = 0.3x \) for the interval \( 0 \leq x \leq 20,000 \):
1. **Closed Circle**: Indicates that the endpoint is included in the function (the value of the function is valid at that point).
2. **Open Circle**: Indicates that the endpoint is not included in the function (the value of the function is not valid at that point).
In your piecewise function:
- The function \( f(x) = 0.3x \) is defined for \( 0 \leq x \leq 20,000 \). This means that when \( x = 0 \), \( f(0) = 0.3(0) = 0 \) is included (thus, a closed circle at \( x = 0 \)), and when \( x = 20,000 \), \( f(20000) = 0.3(20000) = 6000 \) is also included (thus, a closed circle at \( x = 20,000 \)).
Since both endpoints are included in the interval, **both ends should have closed circles**.
Therefore, the correct response is:
**Both ends should have closed circles.**
1. **Closed Circle**: Indicates that the endpoint is included in the function (the value of the function is valid at that point).
2. **Open Circle**: Indicates that the endpoint is not included in the function (the value of the function is not valid at that point).
In your piecewise function:
- The function \( f(x) = 0.3x \) is defined for \( 0 \leq x \leq 20,000 \). This means that when \( x = 0 \), \( f(0) = 0.3(0) = 0 \) is included (thus, a closed circle at \( x = 0 \)), and when \( x = 20,000 \), \( f(20000) = 0.3(20000) = 6000 \) is also included (thus, a closed circle at \( x = 20,000 \)).
Since both endpoints are included in the interval, **both ends should have closed circles**.
Therefore, the correct response is:
**Both ends should have closed circles.**