Question
The graph of a relation is given. Apply the vertical line test to determine if this relation is a function.
(1 point)
Responses
Yes, the given relation is a function.
Yes, the given relation is a function.
No, the given relation is not a function.
No, the given relation is not a function.
The relation is a half-circle.
The relation is a half-circle.
(1 point)
Responses
Yes, the given relation is a function.
Yes, the given relation is a function.
No, the given relation is not a function.
No, the given relation is not a function.
The relation is a half-circle.
The relation is a half-circle.
Answers
Answered by
GPT-4o mini
To determine if a relation is a function using the vertical line test, we draw vertical lines through the graph. If any vertical line intersects the graph at more than one point, then the relation is not a function.
- If the graph is a half-circle, then a vertical line drawn through the circle will intersect it at two points (except at the endpoints of the semicircle). Therefore, this relation does **not** pass the vertical line test.
So, the correct response would be:
**No, the given relation is not a function.**
- If the graph is a half-circle, then a vertical line drawn through the circle will intersect it at two points (except at the endpoints of the semicircle). Therefore, this relation does **not** pass the vertical line test.
So, the correct response would be:
**No, the given relation is not a function.**
Answer
Which of the following is an ordered pair of the relation y=−23x+6 ?(1 point)
Responses
(3,4)
left parenthesis 3 comma 4 right parenthesis
(1,4)
left parenthesis 1 comma 4 right parenthesis
(3,8)
left parenthesis 3 comma 8 right parenthesis
(0,−23)
Responses
(3,4)
left parenthesis 3 comma 4 right parenthesis
(1,4)
left parenthesis 1 comma 4 right parenthesis
(3,8)
left parenthesis 3 comma 8 right parenthesis
(0,−23)
Answered by
GPT-4o mini
To determine which of the given points is an ordered pair of the relation \( y = -23x + 6 \), we can substitute the \( x \)-values of each ordered pair into the equation and see if they yield the corresponding \( y \)-values.
1. For \( (3, 4) \):
\[
y = -23(3) + 6 = -69 + 6 = -63 \quad (\text{not } 4)
\]
2. For \( (1, 4) \):
\[
y = -23(1) + 6 = -23 + 6 = -17 \quad (\text{not } 4)
\]
3. For \( (3, 8) \):
\[
y = -23(3) + 6 = -69 + 6 = -63 \quad (\text{not } 8)
\]
4. For \( (0, -23) \):
\[
y = -23(0) + 6 = 0 + 6 = 6 \quad (\text{not } -23)
\]
None of these ordered pairs yield the correct \( y \)-values based on the equation \( y = -23x + 6 \). Therefore, the answer is that none of the given points are ordered pairs of the relation \( y = -23x + 6 \).
If you have multiple choice options and are looking for one that might be correct based on a miscalculation, please check the values again, as none of the given points satisfy the equation.
1. For \( (3, 4) \):
\[
y = -23(3) + 6 = -69 + 6 = -63 \quad (\text{not } 4)
\]
2. For \( (1, 4) \):
\[
y = -23(1) + 6 = -23 + 6 = -17 \quad (\text{not } 4)
\]
3. For \( (3, 8) \):
\[
y = -23(3) + 6 = -69 + 6 = -63 \quad (\text{not } 8)
\]
4. For \( (0, -23) \):
\[
y = -23(0) + 6 = 0 + 6 = 6 \quad (\text{not } -23)
\]
None of these ordered pairs yield the correct \( y \)-values based on the equation \( y = -23x + 6 \). Therefore, the answer is that none of the given points are ordered pairs of the relation \( y = -23x + 6 \).
If you have multiple choice options and are looking for one that might be correct based on a miscalculation, please check the values again, as none of the given points satisfy the equation.
Answer
Which of the following gives an example of a function that is not linear?(1 point)
Responses
y=x2−3x+2.25
y equals x squared minus 3 x plus 2.25
y=16x+23
y equals Start Fraction 1 over 6 End Fraction x plus Start Fraction 2 over 3 End Fraction
9x+3y−18=0
9 x plus 3 y minus 18 equals 0
2x+3y=16
Responses
y=x2−3x+2.25
y equals x squared minus 3 x plus 2.25
y=16x+23
y equals Start Fraction 1 over 6 End Fraction x plus Start Fraction 2 over 3 End Fraction
9x+3y−18=0
9 x plus 3 y minus 18 equals 0
2x+3y=16
Answered by
GPT-4o mini
To determine which provided option represents a function that is not linear, let's review the given functions:
1. **\( y = x^2 - 3x + 2.25 \)**:
- This is a quadratic function because it includes the \( x^2 \) term. Quadratic functions are not linear.
2. **\( y = 16x + 23 \)**:
- This is a linear function, as it takes the form \( y = mx + b \), where \( m \) and \( b \) are constants.
3. **\( 9x + 3y - 18 = 0 \)**:
- This is a linear equation in standard form. It can be rearranged to \( y = -3x + 6\), which is still linear.
4. **\( 2x + 3y = 16 \)**:
- This is also a linear equation; it can be rearranged to the slope-intercept form \( y = -\frac{2}{3}x + \frac{16}{3} \).
From the evaluations above, the correct answer is:
**\( y = x^2 - 3x + 2.25 \)**, as it is a quadratic function and is not linear.
1. **\( y = x^2 - 3x + 2.25 \)**:
- This is a quadratic function because it includes the \( x^2 \) term. Quadratic functions are not linear.
2. **\( y = 16x + 23 \)**:
- This is a linear function, as it takes the form \( y = mx + b \), where \( m \) and \( b \) are constants.
3. **\( 9x + 3y - 18 = 0 \)**:
- This is a linear equation in standard form. It can be rearranged to \( y = -3x + 6\), which is still linear.
4. **\( 2x + 3y = 16 \)**:
- This is also a linear equation; it can be rearranged to the slope-intercept form \( y = -\frac{2}{3}x + \frac{16}{3} \).
From the evaluations above, the correct answer is:
**\( y = x^2 - 3x + 2.25 \)**, as it is a quadratic function and is not linear.