Question: Is A Circle A Function?

What is the standard form of a circle?

2) The general form : x2 + y2 + Dx + Ey + F = 0, where D, E, F are constants.

If the equation of a circle is in the standard form, we can easily identify the center of the circle, (h, k), and the radius, r .

Note: The radius, r, is always positive.

Example 1: (x-2)2 + (y-3)2 = 4..

What is general equation of circle?

The standard equation of a circle with center at ( a , b ) (a,b) (a,b) and radius r r r is ( x − a ) 2 + ( y − b ) 2 (x-a)^2+(y-b)^2 (x−a)2+(y−b)2= r 2 r^2 r2. If we have a point O = ( a , b ) O=(a,b) O=(a,b) in the plane and a radius r r r, then we can construct a unique circle.

What is the meaning of horizontal line?

Anything parallel to the horizon is called horizontal. As vertical is the opposite of horizontal, anything that makes a 90-degree angle (right angle) with the horizontal or the horizon is called vertical. So, the horizontal line is one that runs across from left to right.

How do you find the function of a circle?

The formula for the equation of a circle is (x – h)2+ (y – k)2 = r2, where (h, k) represents the coordinates of the center of the circle, and r represents the radius of the circle.

Is a curved line a function?

A function can only have one output, y, for each unique input, x. If a vertical line intersects a curve on an xy-plane more than once then for one value of x the curve has more than one value of y, and so, the curve does not represent a function.

What is the horizontal line test used for?

In mathematics, the horizontal line test is a test used to determine whether a function is injective (i.e., one-to-one).

How do you write the standard form of a circle?

The standard form of a circle’s equation is (x-h)² + (y-k)² = r² where (h,k) is the center and r is the radius. To convert an equation to standard form, you can always complete the square separately in x and y.

What is the difference between function and not a function?

A function is a relation between domain and range such that each value in the domain corresponds to only one value in the range. Relations that are not functions violate this definition. They feature at least one value in the domain that corresponds to two or more values in the range.

What is an example of a horizontal line?

An equation that only crosses the y-axis is a horizontal line. … For example: y=5 is a horizontal line that crosses the y-axis at (0,5).

How do you know if a line is vertical?

This relationship is always true: a vertical line will have no slope, and “the slope is undefined” or “the line has no slope” means that the line is vertical. (By the way, all vertical lines are of the form “x = some number”, and “x = some number” means the line is vertical.

How do you know if a function is a function or not?

A WAY easier (and faster), way to know if it is a function is to see if there are two of the same x-intercept (which make a vertical line). If there is, then it is NOT a function.

What is a vertical line?

: a line perpendicular to a surface or to another line considered as a base: such as. a : a line perpendicular to the horizon. b : a line parallel to the sides of a page or sheet as distinguished from a horizontal line.

What is a curved line called?

In mathematics, a curve (also called a curved line in older texts) is an object similar to a line, but that does not have to be straight. … Level curves and algebraic curves are sometimes called implicit curves, since they are generally defined by implicit equations.

What is not a function?

A function is a relation in which each input has only one output. In the relation , y is a function of x, because for each input x (1, 2, 3, or 0), there is only one output y. x is not a function of y, because the input y = 3 has multiple outputs: x = 1 and x = 2.

Which way is vertical line?

The terms vertical and horizontal often describe directions: a vertical line goes up and down, and a horizontal line goes across. You can remember which direction is vertical by the letter, “v,” which points down.

What is the vertical line symbol called?

The vertical line, also called the vertical slash or upright slash ( | ), is used in mathematical notation in place of the expression “such that” or “it is true that.” This symbol is commonly encountered in statements involving logic and sets. Also see Mathematical Symbols.

Is a circle a function vertical line test?

Even though a vertical line through (3,0) or (-3,0) would intersect the circle only once, the Vertical Line Test has to work for every vertical line drawn through the graph. This graph fails the Vertical Line Test, so a circle is not a function.

Is horizontal line a function?

HORIZONTAL LINES – CONSTANT FUNCTIONS Horizontal lines are the graphs of constant functions, those whose values never change no matter what values are acted upon. Any x value produces the same y value as that of all the other x values: the result is constantly the same. The slope of a horizontal line is zero.