How do you shift and reflect a function?

How do you shift and reflect a function?

The function translation / transformation rules:

1. f (x) + b shifts the function b units upward.
2. f (x) − b shifts the function b units downward.
3. f (x + b) shifts the function b units to the left.
4. f (x − b) shifts the function b units to the right.
5. −f (x) reflects the function in the x-axis (that is, upside-down).

What shifts a function?

Definition: Horizontal Shift. Given a function f, a new function g(x)=f(x−h), where h is a constant, is a horizontal shift of the function f. If h is positive, the graph will shift right. If h is negative, the graph will shift left.

What is the reflection of a function?

A reflection is a transformation of the graph of a function over the x-axis or the y-axis (or both). The function retains its basic shape; however, by including a negative sign in the appropriate place in the equation, the graph of the function will flip over one or the other of the axes.

What happens when you shift a function?

This is always true: To shift a function left, add inside the function’s argument: f (x + b) gives f (x)shifted b units to the left. Shifting to the right works the same way; f (x − b) is f (x) shiftedb units to the right.

What does shift mean in math?

A transformation in which a graph or geometric figure is picked up and moved to another location without any change in size or orientation.

What does reflection mean on a graph?

A reflection is a transformation representing a flip of a figure. Figures may be reflected in a point, a line, or a plane. When reflecting a figure in a line or in a point, the image is congruent to the preimage. A reflection maps every point of a figure to an image across a fixed line.

How do you shift 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.

What is reflection in linear algebra?

A reflection is a transformation representing a flip of a figure. Figures may be reflected in a point, a line, or a plane. When reflecting a figure in a line or in a point, the image is congruent to the preimage. A reflection maps every point of a figure to an image across a line of symmetry using a reflection matrix.

What is the difference between a shift and a reflection?

They are shifting and scaling. There are three if you count reflections, but reflections are just a special case of the second translation. A shift is a rigid translation in that it does not change the shape or size of the graph of the function. All that a shift will do is change the location of the graph.

How do you reflect a function on the x axis?

Translations. A function can be reflected about an axis by multiplying by negative one. To reflect about the y-axis, multiply every x by -1 to get -x. To reflect about the x-axis, multiply f(x) by -1 to get -f(x).

How do you reflect a function on a graph?

A function can be reflected about an axis by multiplying by negative one. To reflect about the y-axis, multiply every x by -1 to get -x. To reflect about the x-axis, multiply f (x) by -1 to get -f (x). Putting it all together

What is a vertical shift in math?

Shifts A shift is a rigid translation in that it does not change the shape or size of the graph of the function. All that a shift will do is change the location of the graph. A vertical shift adds/subtracts a constant to/from every y-coordinate while leaving the x-coordinate unchanged.