| {{ 'ml-lesson-number-slides' | message : article.intro.bblockCount }} |
| {{ 'ml-lesson-number-exercises' | message : article.intro.exerciseCount }} |
| {{ 'ml-lesson-time-estimation' | message }} |
Here are a few recommended readings before getting started with this lesson.
The graph of the parent function y=x and the graph of the radical function y=ax−h+k are drawn on the same coordinate plane.
Find the values of a, h, and k.The graph of the function y=x−h+k is shown in the coordinate plane. By changing the values of h and k, observe how the graph is horizontally and vertically translated.
Graph:
Graph:
Graph:
The graphs of the rational function y=x and a vertical or horizontal translation are shown in the coordinate plane.
The graph of the radical function y=acx is shown in the coordinate plane. By changing the values of a and c, observe how the graph is vertically and horizontally stretched and shrunk.
Suppose that a function is horizontally or vertically stretched/shrunk, and that the graphs of the transformed and the original function are both drawn on the same coordinate plane. Then, the values of a or c can be found by following these procedures.
Finding a | Select two points with the same x-coordinate, one point P on the parent function and the other point Q on the transformed function. The value of a is the quotient of the y-coordinate of Q and the y-coordinate of P. |
---|---|
Finding c | Select two points with the same y-coordinate, one point P on the parent function and the other point Q on the transformed function. The value of c is the quotient of the x-coordinate of P and the x-coordinate of Q. |
After mastering vertical and horizontal translations of radical functions, Ignacio is having a hard time understanding vertical and horizontal stretches and shrinks of this type of function. He asked for some help from his very good friend Jordan.
In order to help him, Jordan asks Ignacio to consider the following function.Graph:
Graph:
The graph of the parent function y=x is shown in the coordinate plane. The graph of a horizontal or vertical stretch or shrink is also shown.
Ignacio is now feeling pretty confident about transformations of radical functions again. Now he turns his attention to reflections.
Ignacio considers the following radical function.Graph:
Graph:
Ignacio confidently states that he can now solve any exercise about transformations of radical functions. Jordan skeptically challenges her friend to solve an exercise that combines transformations.
Help Ignacio solve Jordan's challenge!Equation: y=-x+5−6
Graph:
Start by multiplying the output by 2 to find the function that represents the vertical stretch. Then, multiply the input by -1 to reflect the graph in the y-axis. Finally, subtract 3 units from the input.
To help Ignacio, the transformations will be applied one at a time.
With the topics learned in this lesson, the challenge presented at the beginning can be solved. The graphs of the radical function y=ax−h+k and its corresponding