How can you use transformations to graph a function?
Key Takeaways
- 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 use transformations of a function?
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.
- f (x – b) shifts the function b units to the right.
- –f (x) reflects the function in the x-axis (that is, upside-down).
How do you find the transformation of a graph?
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 are the transformations of a graph?
Transformations of Function Graphs | |
---|---|
-f (x) | reflect f (x) over the x-axis |
f (x – k) | shift f (x) right k units |
k•f (x) | multiply y-values by k (k > 1 stretch, 0 < k < 1 shrink vertical) |
f (kx) | divide x-values by k (k > 1 shrink, 0 < k < 1 stretch horizontal) |
How do you translate a graph?
Transformations of Graphs
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. if k < 0, the base graph shifts k units downward.
How do you write a rule for translation?
Mapping Rule A mapping rule has the following form (x,y) → (x−7,y+5) and tells you that the x and y coordinates are translated to x−7 and y+5. Translation A translation is an example of a transformation that moves each point of a shape the same distance and in the same direction.
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. Scroll down the page for more examples and solutions.
How do you describe transformation?
A transformation is a process that manipulates a polygon or other two-dimensional object on a plane or coordinate system. Mathematical transformations describe how two-dimensional figures move around a plane or coordinate system. A preimage or inverse image is the two-dimensional shape before any transformation.
What are the 8 types of functions?
The eight types are linear, power, quadratic, polynomial, rational, exponential, logarithmic, and sinusoidal.
What are the 12 basic functions?
- The Identity Function. Domain: ______________________
- The Squaring Function. Domain: ______________________
- The Cubing Function. Domain: ______________________
- The Square Root Function. Domain: ______________________
- The Natural Logarithm Function.
- The Reciprocal Function.
- The Exponential Function.
- The Sine Function.
What are some examples of transformation?
What are some examples of energy transformation?
- The Sun transforms nuclear energy into heat and light energy.
- Our bodies convert chemical energy in our food into mechanical energy for us to move.
- An electric fan transforms electrical energy into kinetic energy.
How do you translate a graph to the right?
To move a graph right, we add a negative value to the x-value. To move a graph left, we add a positive value to the x-value. To stretch a graph in the y-axis, we multiply the whole function times any number n such that n > 1.