Table of Contents
- 1 What is the rule for transformation over the X axis?
- 2 What has to be true if you have a transformation of reflection over the x axis?
- 3 What is the rule for transformation?
- 4 What is the rule for translations?
- 5 How do you calculate transformations?
- 6 What axis is the triangle being reflected over?
- 7 What are the 4 translations?
- 8 Which is the axis of reflection in a reflection transformation?
- 9 How is a function related to the x axis?
- 10 Are there matrices for reflections over the Y axis?
What is the rule for transformation over the X axis?
The rule for reflecting over the X axis is to negate the value of the y-coordinate of each point, but leave the x-value the same. For example, when point P with coordinates (5,4) is reflecting across the X axis and mapped onto point P’, the coordinates of P’ are (5,-4).
What has to be true if you have a transformation of reflection over the x axis?
When you reflect a point across the x-axis, the x-coordinate remains the same, but the y-coordinate is transformed into its opposite (its sign is changed). If you forget the rules for reflections when graphing, simply fold your paper along the x-axis (the line of reflection) to see where the new figure will be located.
When you reflect an object over the X axis what happens?
When reflecting objects across the x-axis, the x-values of each original point will remain the same and the y-values will become opposite.
What is the rule for transformation?
The function translation / transformation rules: f (x) + b shifts the function b units upward. f (x) – b shifts the function b units downward. f (x + b) shifts the function b units to the left.
What is the rule for translations?
✓ Translations can be achieved by performing two composite reflections over parallel lines. ✓ Translations are isometric, and preserve orientation. Coordinate plane rules: (x, y) → (x ± h, y ± k) where h and k are the horizontal and vertical shifts. Note: If movement is left, then h is negative.
How can you tell if a graph is transformation?
- Identifying transformations allows us to quickly sketch the graph of functions.
- If a positive constant is added to a function, f(x)+k, the graph will shift up.
- If a positive constant is added to the value in the domain before the function is applied, f(x+h), the graph will shift to the left.
How do you calculate transformations?
Here are some things we can do:
- Move 2 spaces up:h(x) = 1/x + 2.
- Move 3 spaces down:h(x) = 1/x − 3.
- Move 4 spaces right:h(x) = 1/(x−4) graph.
- Move 5 spaces left:h(x) = 1/(x+5)
- Stretch it by 2 in the y-direction:h(x) = 2/x.
- Compress it by 3 in the x-direction:h(x) = 1/(3x)
- Flip it upside down:h(x) = −1/x.
What axis is the triangle being reflected over?
Triangle GHI is reflected across the x-axis.
What are the 3 things needed to complete a rotation transformation?
To perform a geometry rotation, we first need to know the point of rotation, the angle of rotation, and a direction (either clockwise or counterclockwise). A rotation is also the same as a composition of reflections over intersecting lines.
What are the 4 translations?
There are four main types of transformations: translation, rotation, reflection and dilation. These transformations fall into two categories: rigid transformations that do not change the shape or size of the preimage and non-rigid transformations that change the size but not the shape of the preimage.
Which is the axis of reflection in a reflection transformation?
In a reflection transformation, all the points of an object are reflected or flipped on a line called the axis of reflection or line of reflection. A reflection is defined by the axis of symmetry or mirror line.
What causes a graph to reflect across the x axis?
Another effect of ” a ” is to reflect the graph across the x -axis. When the parent function f (x) = x2 has an a -value that is less than 0, the graph reflects across the x -axis before it is transformed. The graph below represents the function f (x) = – x2.
Graph functions using reflections about the x-axis and the y-axis Another transformation that can be applied to a function is a reflection over the x – or y -axis. A vertical reflection reflects a graph vertically across the x -axis, while a horizontal reflection reflects a graph horizontally across the y -axis.
Are there matrices for reflections over the Y axis?
Matrices for Reflections over the y-axis and x-axis. Matrices for Reflections over the line y = x. Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.