Consider the equation x^2+(y-2)^2=1 and the relation “(x, y) R (0, 2)”, where R is read as “has distance 1 of”. For example, “(0, 3) R (0, 2)”, that is, “(0, 3) has distance 1 of (0, 2)”. This relation can also be read as “the point (x, y) is on the circle of radius 1 with center (0, 2)”. In other words: “(x, y) satisfies this equation
1. Does this equation determine a relation between x and y?
Yes, we can say that this equation determines a relationship between x and y. For a circle of radius 1 centered at (0, 2), the relationship between x and y is the equation for the circle. But to find the value of x or y, we need to apply the formula
When a = 0, b = 2, r = 1
2. Can the variable x can be seen as a function of y, like x=g(y)?
Yes, the variable x can be seen as a function of y, like x=g(y).
x = g(y)
3. Can the variable y be expressed as a function of x, like y= h(x)?
Yes, the variable y be expressed as a function of x, like y= h(x).
y= h(x)
4. If these are possible, then what will be the domains for these two functions?
x = g(y)
So, the domain for x = g(y) is
(1,3)
y = h(x)
So, the domain for y = h(x) is
(-1,1)
5. What are the graphs of these two functions?
The graphs of the two functions show a semicircle centered at (0,2).
6. Are there points of the coordinate axes that relate to (0, 2) by means of R?
Yes. This is because every point on the circle is associated with a distance (0, 2) to the center by means of R.
middle point (0, 2)
y=h(x) (0,3)
x=g(y) (0,1)
(377 words except for question texts)
References
Abramson, J. (2017). Algebra and trigonometry. OpenStax, TX: Rice University. Retrieved from https://openstax.org/details/books/algebra-and-trigonometry
댓글