Look at the attached image (credit to Desmos graphing calculator)
To graph the equation y=4x+1, we just find two points that exist, plot them, and draw a straight line that goes through them.
Let's try x=0:
One point on the line is (0,1)
Let's try x=1:
Another point is (1,5).
Now, plot these two points and draw a line through them.
Answer:
3.5
−2.46
1.16 error aligning the decimal point.
Do this instead
3.50
- 2.46
1.04
You can describe the domain by every possible x value in the function, since that function has a vertical intersection line which means the x value will never pass it on the negative side, the domain would be from -2 to all the postive numbers, X > -2 or (-2,∞).
For the range, simply it's all the possible y values. In that function it's impossible to go under 0 or negative value. That means the range would be Y>0 or (0,∞).
If you want to know if it's a function or not you could try the vertical line test, select any x value and draw straight line on it, if the line crosses 2 y points in the same x value it wont be a function, In your case each x value has it's own Y value.
So the answer is Domain x>-2; Range y>0; Yes, it is a function
and 
are the <em>farthest</em> from the origin and 
is the <em>closest</em> from the origin.
Let be a curve of the form 
. The distance with respect to origin is found by using the following Pythagorean identity:
(1)
Where 
is the square distance function.
We can modify (1) as following:
![r = [27-3\cdot (y-2)^{2}]+y^{2}](https://tex.z-dn.net/?f=r%20%3D%20%5B27-3%5Ccdot%20%28y-2%29%5E%7B2%7D%5D%2By%5E%7B2%7D)
(1b)
Now we apply the First and second derivative tests to determine the minimum and maximum distances from the origin:
First derivative test
Second derivative test
The y-component represents a maximum.
Now we graph the function with the ressource of a graphing tool, we find the following points:
Farthest points: , .
Closest points: .
and are the <em>farthest</em> from the origin and is the <em>closest</em> from the origin.
To learn more on ellipses, we kindly invite to check this verified question: brainly.com/question/19507943
