Asked by bigepic

Find the output of the function y=−3x−7
when the input is −5
. (1 point)
Answered by bigepic
Find the value of the function y=3x2−21
when x=4
.(1 point)
Answered by bigepic
An illustration shows a coordinate plane with four quadrants. The x and y axes range from negative 6 to 6 in increments of 1. A semicircle is graphed on the plane. The semicircle passes through points plotted at coordinates left parenthesis negative 5 comma 0 right parenthesis, left parenthesis 0 comma 5 right parenthesis, and left parenthesis 5 comma 0 right parenthesis.
The graph of a relation is given. Apply the vertical line test to determine if this relation is a function. Enter 1 if the relation is a function. Enter 2 if the relation is not a function.(1 point)
Answered by bigepic
wrong its 1
Answered by bigepic
Which of the following functions is proportional?

Function 1: y=x2

Function 2: y=2x

Function 3: y=x+2
(1 point)
Answered by bigepic
When the input is x=0.3
, which of the following is the output of the function y=3x+6
?(1 point)
Responses
Answered by bigepic
What is the value of the function y=1/8x−13
when x=−4
?(1 point)
Answered by bigepic
An illustration shows a coordinate plane with four quadrants. The x and y axes range from negative 6 to 6 in increments of 1. A semicircle is graphed on the plane. The semicircle passes through points plotted at coordinates left parenthesis 0 comma 6 right parenthesis, left parenthesis 6 comma 0 right parenthesis, and left parenthesis 0 comma negative 6 right parenthesis.
The graph of a relation is given. Apply the vertical line test to determine if this relation is a function.
Answered by bigepic
Which of the following is an ordered pair of the relation y=−2/3x+6
?(1 point)(3,4)
left parenthesis 3 comma 4 right parenthesis

(3,8)
left parenthesis 3 comma 8 right parenthesis

(1,4)
left parenthesis 1 comma 4 right parenthesis

(0,−2/3)
Answered by bigepic
dentify which of the following functions is proportional.(1 point)
Responses

y=12x
y equals Start Fraction 1 over 2 End Fraction x

y=x2
y equals x squared

y=12x
y equals Start Fraction 1 over 2 x End Fraction

y=x+12
Answered by GPT-4o mini
To find the output of the function \( y = -3x - 7 \) when the input \( x = -5 \), we can substitute \(-5\) into the equation.

\[
y = -3(-5) - 7
\]

Now, calculate the multiplication:

\[
y = 15 - 7
\]

Then, perform the subtraction:

\[
y = 8
\]

Therefore, the output of the function when the input is \(-5\) is \( y = 8 \).
Answered by GPT-4o mini
To find the value of the function \( y = 3x^2 - 21 \) when \( x = 4 \), we can substitute \( 4 \) into the equation.

\[
y = 3(4^2) - 21
\]

First, calculate \( 4^2 \):

\[
4^2 = 16
\]

Then, substitute that value back into the equation:

\[
y = 3(16) - 21
\]

Next, perform the multiplication:

\[
y = 48 - 21
\]

Finally, perform the subtraction:

\[
y = 27
\]

Therefore, the value of the function when \( x = 4 \) is \( y = 27 \).
Answered by GPT-4o mini
To determine if the relation represented by the semicircle is a function, we can apply the vertical line test.

The vertical line test states that if a vertical line crosses the graph of the relation at more than one point, then the relation is not a function.

Since the semicircle is a portion of a circle, a vertical line can be drawn that intersects it at two points. For example, if you draw a vertical line at \( x = 0 \), it will intersect the semicircle at the points \( (0, 5) \) and \( (0, -5) \) (the latter point is not actually plotted as it is in the semicircle's lower part).

Since there are vertical lines that intersect the graph at more than one point, the relation is **not a function**.

Therefore, you should enter **2** (the relation is not a function).
Answered by GPT-4o mini
I apologize for any confusion, but let me clarify the vertical line test applied to the semicircle graph:

A semicircle, defined as the upper half of a circle (in this case, from points like \( (-5, 0) \), \( (0, 5) \), and \( (5, 0) \)), does not pass the vertical line test because a vertical line drawn anywhere within the range from \( x = -5 \) to \( x = 5 \) will intersect the semicircle at exactly one point on the top.

Thus, a semicircle does indeed represent a function because for every input (x-value), there is exactly one output (y-value).

Given this, if the vertical line test shows that it passes (i.e., each vertical line intersects the graph at most once), then the correct answer should be that it **is** a function.

Therefore, the answer is indeed \( 1 \) (the relation **is** a function). Thank you for your patience, and I appreciate your feedback!
Answered by GPT-4o mini
A function is considered proportional if it can be expressed in the form \( y = kx \), where \( k \) is a constant. This means that the relationship between \( x \) and \( y \) is linear and passes through the origin (0, 0).

Let's analyze the given functions:

1. **Function 1: \( y = x^2 \)**:
- This is a quadratic function and does not represent a linear relationship. Therefore, it is **not** proportional.

2. **Function 2: \( y = 2x \)**:
- This is a linear function in the form \( y = kx \) where \( k = 2 \). It represents a proportional relationship because it passes through the origin (0, 0). Therefore, it **is** proportional.

3. **Function 3: \( y = x + 2 \)**:
- This is a linear function, but it does not pass through the origin (when \( x = 0 \), \( y = 2 \)). Therefore, it is **not** proportional.

The only proportional function among the options is **Function 2: \( y = 2x \)**.

Thus, the answer is **Function 2**.
Answered by GPT-4o mini
To find the output of the function \( y = 3x + 6 \) when the input \( x = 0.3 \), we substitute \( 0.3 \) into the equation.

\[
y = 3(0.3) + 6
\]

First, calculate \( 3 \times 0.3 \):

\[
3(0.3) = 0.9
\]

Now, add \( 6 \) to that result:

\[
y = 0.9 + 6 = 6.9
\]

Therefore, the output of the function when the input is \( x = 0.3 \) is \( y = 6.9 \).
Answered by GPT-4o mini
To find the value of the function \( y = \frac{1}{8}x - 13 \) when \( x = -4 \), we substitute \(-4\) into the equation.

\[
y = \frac{1}{8}(-4) - 13
\]

First, calculate \( \frac{1}{8} \times (-4) \):

\[
y = -\frac{4}{8} - 13
\]

Simplifying \(-\frac{4}{8}\):

\[
-\frac{4}{8} = -\frac{1}{2}
\]

Now, substituting this back in:

\[
y = -\frac{1}{2} - 13
\]

Next, we need to express \( -13 \) in terms of halves to combine the fractions:

\[
-13 = -\frac{26}{2}
\]

So we can rewrite the equation:

\[
y = -\frac{1}{2} - \frac{26}{2}
\]

Now, combine the fractions:

\[
y = -\frac{1 + 26}{2} = -\frac{27}{2}
\]

Thus, the value of the function when \( x = -4 \) is:

\[
y = -\frac{27}{2} \text{ or } -13.5
\]

So the final answer is:
\[
\boxed{-\frac{27}{2}} \text{ or } -13.5
\]
Answered by GPT-4o mini
To determine if the relation represented by the semicircle is a function using the vertical line test, we consider the following:

The vertical line test states that if any vertical line drawn through the graph intersects the graph at more than one point, then the relation is **not** a function. Conversely, if every vertical line intersects the graph at most once, the relation **is** a function.

In your description, the semicircle passes through the points \( (0, 6) \), \( (6, 0) \), and \( (0, -6) \). However, the important characteristic of this semicircle is that it represents either the upper or the lower half of a circle.

1. If the semicircle is positioned such that it includes the points \( (0, 6) \) and \( (6, 0) \), then it is likely the **upper** semicircle of a circle centered on the y-axis, above the x-axis. In this case:

- Any vertical line drawn within the domain of the circle (i.e., between \( x = -6 \) and \( x = 6 \)) will intersect the semicircle exactly once.

2. Conversely, if you intended to describe a full circle which includes points like \( (0, -6) \) as well, then it consists of both the upper and lower halves. In that scenario, a vertical line drawn at any position except the center (where \( x = 0 \)) would intersect at two points, which would mean it is **not** a function.

Considering your mention of it being a semicircle (as initially stated in previous messages), it suggests it is only the upper part (passing through \( (0, 6) \) and \( (6, 0) \)), which confirms that it does pass the vertical line test.

**Conclusion:** If we are indeed dealing with a semicircle (the upper half), then:

- **The relation is a function.**

Thus, based on the vertical line test, the answer would be **1** (the relation is a function). If it included the lower half and was interpreted as a full circle, then the answer would change to **2** (the relation is not a function).

It is important to confirm whether you are referring specifically to the upper or lower semicircle in this context.
Answered by GPT-4o mini
To determine which of the given ordered pairs is a point on the line defined by the equation \( y = -\frac{2}{3}x + 6 \), we can substitute each x-coordinate of the ordered pairs into the equation and see if the output y matches the y-value of the ordered pair.

1. **For the pair \( (3, 4) \)**:
\[
y = -\frac{2}{3}(3) + 6 = -2 + 6 = 4
\]
The output matches, so \( (3, 4) \) **is** an ordered pair on the relation.

2. **For the pair \( (3, 8) \)**:
The x-value is still 3. We already calculated that for \( x = 3 \), \( y = 4 \). Since this does not match, \( (3, 8) \) **is not** an ordered pair on the relation.

3. **For the pair \( (1, 4) \)**:
\[
y = -\frac{2}{3}(1) + 6 = -\frac{2}{3} + 6 = -\frac{2}{3} + \frac{18}{3} = \frac{16}{3} \approx 5.33
\]
Since the output does not match \( 4 \), \( (1, 4) \) **is not** an ordered pair on the relation.

4. **For the pair \( (0, -\frac{2}{3}) \)**:
\[
y = -\frac{2}{3}(0) + 6 = 0 + 6 = 6
\]
Since the output does not match \( -\frac{2}{3} \), \( (0, -\frac{2}{3}) \) **is not** an ordered pair on the relation.

**Conclusion:** The only ordered pair that is on the relation defined by the equation \( y = -\frac{2}{3}x + 6 \) is **(3, 4)**.
Answered by GPT-4o mini
To determine which of the given functions is proportional, we need to identify functions that have a constant ratio between \( y \) and \( x \), which can be expressed in the form \( y = kx \), where \( k \) is a constant.

Let's analyze the given functions one by one:

1. **\( y = 12x \)**:
- This is in the form \( y = kx \) where \( k = 12 \). It is a proportional relationship.

2. **\( y = \frac{1}{2}x \)**:
- This is also in the form \( y = kx \) where \( k = \frac{1}{2} \). It is also a proportional relationship.

3. **\( y = x^2 \)**:
- This is a quadratic function and does not fit the form \( y = kx \). Therefore, it is **not** proportional.

4. **\( y = \frac{1}{2}x \)**:
- This is the same as a previous option; it is in the form \( y = kx \) where \( k = \frac{1}{2} \). It is a proportional relationship.

5. **\( y = x + 12 \)**:
- This is a linear function, but it does not pass through the origin (as it has a y-intercept of 12). Therefore, it is **not** proportional.

**Conclusion:** The functions that are proportional are:

- \( y = 12x \)
- \( y = \frac{1}{2}x \)

So, the answer is:
- \( y = 12x \) **and** \( y = \frac{1}{2}x \) are both proportional functions.