Look at this flower. Like most flowers, the petals are similar-looking to each other.
A simple way to draw this flower is by first drawing one petal, and then use copies of the first petal transformed in appropriate way to produce more petals.
One such transformation, used here, is to stretch part of the petal horizontally by different amounts to get more petals.
If a coordinate system is used, mathematical techniques can be used to carry out the transformations and draw the additional petals.
Let’s learn about transformations using graphical functions. The graph of y equal x squared minus three, resembles part of a petal.
To make a wider petal, replace x in the expression for the graph with zero point five x.
This can be done by moving the horizontal slider to the left so that the value zero point five appears in the accompanying box.
Note that the modified function appears in the modified function box. You can also enter zero point five directly into the box and press Enter.
To make an even wider petal, use a smaller value for the multiplier, either by moving the horizontal slider farther to the left or by entering a value less than zero point five. Smaller values make for wider petals, stretching the graph to the left and right. You can also use larger multipliers, either by typing them directly into the box and pressing enter or by moving the horizontal slider to the right. Instead of stretching the graph, it is shrunk against the y-axis. Multiplying the x-value by different numbers before plugging into the expression affects the graph in one way, stretching or shrinking it horizontally depending on the value of the multiplier. but it is also possible to affect the graph another way. By changing the position of the vertical slider, changes of a slightly different nature can be made. Note that when the entire function is multiplied by zero point five, the points are half as far away from the x-axis as the original graph. For instance, the lowest point on the graph has moved from negative three on the y-axis to negative one point five A smaller multiplier moves the points even closer to the x-axis. Again, you can use the slider or you can enter values into the boxes and press enter. The graph is being shrunk vertically instead of horizontally. If all of the points need to be farther from the x-axis instead, a larger multiplier can be used. Larger multipliers move points up or down farther from the x-axis, stretching the graph vertically instead of shrinking it. Multiplying the entire function by different numbers after evaluating the expression affects the graph in a manner different than multiplying just the x-value before evaluating the expression.