pls. explain transformations on functions..
LOL, you have to be a bit more specific than that.
exponential and the cubic root function :)
thanks
for example graph e^(x)
and then e^(5*x)
note you have to be really careful about using parentheses and * for "times" when using graphing software)
try x and x^(1/3)
Sure! Transformations on functions refer to changes made to the shape, position, or size of a function's graph. These transformations can be applied to various types of functions, such as linear, quadratic, exponential, logarithmic, etc.
There are four primary types of transformations:
1. Translation (Shift): This transformation involves moving the entire graph of a function horizontally or vertically. It is represented by adding or subtracting a value to the original function. Shifting the graph to the right is achieved by subtracting a value from the input, whereas shifting it to the left is achieved by adding a value to the input. Similarly, shifting the graph upwards is achieved by adding a value to the output, while shifting it downwards is achieved by subtracting a value from the output.
2. Reflection: This transformation involves flipping the graph of the function across a specific axis. Reflection across the x-axis can be achieved by negating the output (y-coordinate) of each point on the graph. Reflection across the y-axis is achieved by negating the input (x-coordinate) of each point.
3. Scaling (Stretching/Compressing): This transformation involves changing the size of the graph of a function. Scaling can occur horizontally or vertically, or even in both directions simultaneously. Horizontal scaling, also known as stretching or compressing, is achieved by multiplying or dividing the input values (x-coordinates) of each point on the graph. Vertical scaling is achieved by multiplying or dividing the output values (y-coordinates) of each point.
4. Vertical Shift (Change in Amplitude): This transformation involves changing the vertical position or amplitude of the function's graph. It is achieved by adding or subtracting a constant value to the output (y-coordinate) of each point.
To apply transformations to a function, follow these steps:
1. Identify the original function, usually denoted by f(x) or y = f(x).
2. Determine the specific type of transformation required (translation, reflection, scaling, vertical shift).
3. Apply the necessary mathematical operations and values to the original function based on the type of transformation.
4. Simplify the resulting function (if necessary) to obtain the transformed function.
5. Graph the transformed function to observe the changes made to the original graph.
Remember that the order in which you apply transformations can affect the final result. It's important to follow the rules for each type of transformation and understand how they impact the function.
Gee, I am not sure how to transform either into anything other than themselves. You can stretch them or move them. Try a graphing program like
http://www.wolframalpha.com/examples/PlottingAndGraphics.html