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Asked by: Bennett Koelpin
Updated: 21 July 2021 01:00:00 PM

How to translate a circle?

ANSWER: The center of the given circle is at the origin. The translated center will be shifted 6 units to the right and 3 units down, placing it at (6,-3). The circle has a radius of 4. The equation will be (x - 6)2 + (y + 3)2 = 16.

Taking this into account how do you transform a circle?

Dilation To dilate a circle, we start with our standard equation: x2+y2=r2 To dilate the circle we multiply our desired factor squared into the right side of the equation. For example, two multiply the diameter of the circle by two, our equation would now be x2+y2=22(r2).

Taking into account what is the parent equation of a circle?

The equation of a circle appears as (x – h)2 + (y – v)2 = r2. This is called the center-radius form (or standard form) because it gives you both pieces of information at the same time. The h and v represent the coordinates of the center of the circle being at the point (h, v), and r represents the radius.

In the same vein is a circle a function?

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.
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Related questions and answers

What is the slope of a vertical line?

The slope of a line is change in Y / change in X. The slope of a horizontal line = 0, not undefined. The slope of a vertical line = undefined.

Why is a circle a circle?

A circle is a plane figure bounded by one curved line, and such that all straight lines drawn from a certain point within it to the bounding line, are equal. The bounding line is called its circumference and the point, its centre.

What is the vertical line symbol called?

The vertical bar, | , is a glyph with various uses in mathematics, computing, and typography. It has many names, often related to particular meanings: Sheffer stroke (in logic), pipe, vbar, stick, vertical line, vertical slash, bar, pike, or verti-bar, and several variants on these names.

Would a circle on a graph be a function?

The first graph is a circle, the second is an ellipse, the third is two straight lines, and the fourth is a hyperbola. In each example, there are values of x for which there are two values of y. So these are not graphs of functions.

What is the name for a half circle?

In mathematics (and more specifically geometry), a semicircle is a one-dimensional locus of points that forms half of a circle. The full arc of a semicircle always measures 180° (equivalently, π radians, or a half-turn).

Is a chord always a diameter?

Why a diameter is the longest chord in a circle? A segment of a straight line joining two points on a circle is called a chord; a chord that passes through the center of the circle is called a diameter. (Ambiguously, the word "diameter" also denotes the length of a diameter.)

What line has a slope of 0?

A horizontal line has slope zero since it does not rise vertically (i.e. y1 − y2 = 0), while a vertical line has undefined slope since it does not run horizontally (i.e. x1 − x2 = 0).

What do you do when the slope is 0?

The Graph Of A Zero-Slope Line
Just take the standard linear equation (Y = mx + B) and drop off the X since there is no movement on the X-axis. This means that the equation is Y = 0X + b, or just Y = b once you've eliminated the X (since anything multiplied by zero is always zero).

How do you tell if a slope is horizontal or vertical?

Note that when a line has a positive slope it rises up left to right. Note that when a line has a negative slope it falls left to right. Note that when a line is horizontal the slope is 0. Note that when the line is vertical the slope is undefined.

What is the equation of a vertical line?

Vertical Lines
Thus, the equation for a vertical line is x = a, where a is the value that x takes.

What does a 0 slope look like?

Lesson Summary
' When the 'rise' is zero, then the line is horizontal, or flat, and the slope of the line is zero. Put simply, a zero slope is perfectly flat in the horizontal direction. The equation of a line with zero slope will not have an x in it. It will look like 'y = something.

What are 4 types of slopes?

Slopes come in 4 different types: negative, positive, zero, and undefined. as x increases.

Why is circle not a function?

If you are looking at a function that describes a set of points in Cartesian space by mapping each x-coordinate to a y-coordinate, then a circle cannot be described by a function because it fails what is known in High School as the vertical line test. A function, by definition, has a unique output for every input.

What is the standard form of a circle?

Standard form for the equation of a circle is (x−h)2+(y−k)2=r2. The center is (h,k) and the radius measures r units.

How do I find the slope of the line?

The slope of a line characterizes the direction of a line. To find the slope, you divide the difference of the y-coordinates of 2 points on a line by the difference of the x-coordinates of those same 2 points.

Why the vertical line test determines if a graph is a function?

The vertical line test can be used to determine whether a graph represents a function. If we can draw any vertical line that intersects a graph more than once, then the graph does not define a function because a function has only one output value for each input value.

What is the only type of straight line that would fail the vertical line test?

Answer: B) vertical line
A vertical line has all points with the same x coordinate, but infinitely many different y coordinates. It inherently fails the vertical line test because we can pass a single straight line through more than one point on the function curve.

What does a positive slope look like?

What the Slope Means. A positive slope means that two variables are positively related—that is, when x increases, so does y, and when x decreases, y decreases also. Graphically, a positive slope means that as a line on the line graph moves from left to right, the line rises.

How do you tell if a graph represents a function?

Use the vertical line test to determine whether or not a graph represents a function. If a vertical line is moved across the graph and, at any time, touches the graph at only one point, then the graph is a function. If the vertical line touches the graph at more than one point, then the graph is not a function.

Is half a circle a function?

Function defined by a relation in the form f(x) = √r2–x2 or f(x) = − √r2–x2 where r is the radius of a circle centered on the origin point.

Can a vertical line be a function?

For a relation to be a function, use the Vertical Line Test: Draw a vertical line anywhere on the graph, and if it never hits the graph more than once, it is a function. If your vertical line hits twice or more, it's not a function.

How do you know if a slope is zero?

Zero slope
  1. Any line of the form y=c, where c is some real number, will have a slope of zero.
  2. Let's use the line graphed above, y=2, to understand why a line like this will always have zero slope.
  3. Every point on the line y=2 has a y-coordinate of 2.
  4. For other vertical lines, y=c, the y-coordinates will always be c.