Question
Determine if the relation y = 3x + 1 is a function by first graphing the relation, then applying the vertical test. Is this equation a function, yes or no?
Answers
Answer
Determine if 6x^2 + y = 7 is a linear or nonlinear function.
Answered by
GPT 3.5
To graph the relation y = 3x + 1, we can first plot a few points to see the pattern:
When x = 0, y = 3(0) + 1 = 1
When x = 1, y = 3(1) + 1 = 4
When x = 2, y = 3(2) + 1 = 7
Plotting these points on a graph, we can see that the points lie on a straight line:
```
(0, 1)
(1, 4)
(2, 7)
```
The vertical test states that for a relation to be a function, every vertical line passing through the graph should only intersect in one point.
In this case, since the relation y = 3x + 1 is a straight line, every vertical line will only intersect the line at one point. Therefore, this graph passes the vertical test and y = 3x + 1 is indeed a function.
Therefore, the equation y = 3x + 1 is a function.
When x = 0, y = 3(0) + 1 = 1
When x = 1, y = 3(1) + 1 = 4
When x = 2, y = 3(2) + 1 = 7
Plotting these points on a graph, we can see that the points lie on a straight line:
```
(0, 1)
(1, 4)
(2, 7)
```
The vertical test states that for a relation to be a function, every vertical line passing through the graph should only intersect in one point.
In this case, since the relation y = 3x + 1 is a straight line, every vertical line will only intersect the line at one point. Therefore, this graph passes the vertical test and y = 3x + 1 is indeed a function.
Therefore, the equation y = 3x + 1 is a function.
Answered by
GPT 3.5
To determine if the equation 6x^2 + y = 7 is a linear or nonlinear function, we can rewrite it in the standard form of a linear function, which is y = mx + b.
First, subtract 6x^2 from both sides of the equation:
y = -6x^2 + 7
This equation is not in the form y = mx + b, which is the standard form of a linear function. In this form, the variable x should only have a power of 1 and y should be raised to the power of 1 as well.
Since the equation y = -6x^2 + 7 contains a squared term (x^2), it is nonlinear.
Therefore, the equation 6x^2 + y = 7 is a nonlinear function.
First, subtract 6x^2 from both sides of the equation:
y = -6x^2 + 7
This equation is not in the form y = mx + b, which is the standard form of a linear function. In this form, the variable x should only have a power of 1 and y should be raised to the power of 1 as well.
Since the equation y = -6x^2 + 7 contains a squared term (x^2), it is nonlinear.
Therefore, the equation 6x^2 + y = 7 is a nonlinear function.