 # Quick Answer: How Do You Translate A Graph?

## How do you translate a function on a graph?

The graph of a function can be moved up, down, left, or right by adding to or subtracting from the output or the input.

Adding to the output of a function moves the graph up.

Subtracting from the output of a function moves the graph down..

## How do you know when a graph is translated up or down?

The Rule for Vertical Translations: if y = f(x), then y = f(x) + k gives a vertical translation. The translation k moves the graph upward when k is a postive value and downward when k is negative value.

## How do you shift a graph?

The simplest shift is a vertical shift, moving the graph up or down, because this transformation involves adding a positive or negative constant to the function. In other words, we add the same constant to the output value of the function regardless of the input.

## What is the standard equation of a circle?

We know that the general equation for a circle is ( x – h )^2 + ( y – k )^2 = r^2, where ( h, k ) is the center and r is the radius. So add 21 to both sides to get the constant term to the righthand side of the equation. Then complete the square for the y terms.

## How do you shift a graph vertically?

Vertically translating a graph is equivalent to shifting the base graph up or down in the direction of the y-axis. A graph is translated k units vertically by moving each point on the graph k units vertically. g (x) = f (x) + k; can be sketched by shifting f (x) k units vertically.

## How do you translate a graph horizontally?

Horizontally translating a graph is equivalent to shifting the base graph left or right in the direction of the x-axis. A graph is translated k units horizontally by moving each point on the graph k units horizontally. g(x) = f (x – k), can be sketched by shifting f (x) k units horizontally.

## How do you translate a circle on a graph?

follow these steps:Realize that the circle is centered at the origin (no h and v) and place this point there.Calculate the radius by solving for r. Set r-squared = 16. … Plot the radius points on the coordinate plane. … Connect the dots to graph the circle using a smooth, round curve.

## What’s the rule for translation?

The second notation is a mapping rule of the form (x,y) → (x−7,y+5). This notation tells you that the x and y coordinates are translated to x−7 and y+5. The mapping rule notation is the most common. Sarah describes a translation as point P moving from P(−2,2) to P (1,−1).

## How do you move a graph vertically and horizontally?

The vertical shift results from a constant added to the output. Move the graph up for a positive constant and down for a negative constant. The horizontal shift results from a constant added to the input. Move the graph left for a positive constant and right for a negative constant.

## What is transformation of a graph?

Graph transformation is the process by which an existing graph, or graphed equation, is modified to produce a variation of the proceeding graph. It’s a common type of problem in algebra, specifically the modification of algebraic equations.

## What equation makes a circle on a graph?

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.

## What are the 7 parent functions?

The following figures show the graphs of parent functions: linear, quadratic, cubic, absolute, reciprocal, exponential, logarithmic, square root, sine, cosine, tangent.

## How do you reflect a graph?

How To: Given a function, reflect the graph both vertically and horizontally.Multiply all outputs by –1 for a vertical reflection. The new graph is a reflection of the original graph about the x-axis.Multiply all inputs by –1 for a horizontal reflection.