The graph of a relation is given. Apply the vertical line test to determine if this relation is a function.

Question

(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.

Answer 1

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.

Answer 2

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)

Answer 3

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.

Answer 4

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

Answer 5

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.