An electric device delivers a current of [tex]$15.0 A$[/tex] for 30 seconds. How many electrons flow through it?
Answer (1)
Substitute arbitrary values for h and k to define a transformed function.
Choose h = 2 and k = 3 as an example.
Substitute these values into the equation y = 3 x − h − k .
The resulting transformed function is y = 3 x − 2 − 3 .
Explanation
Understanding the Problem The problem asks us to replace the variables h and k in the equation y = 3 x − h − k to define a specific transformed function. Since no specific values are provided for h and k , we will choose arbitrary values to demonstrate the transformation.
Choosing Values for h and k Let's choose h = 2 and k = 3 . These values will shift the cube root function horizontally by 2 units and vertically by 3 units.
Substituting the Values Substitute h = 2 and k = 3 into the equation y = 3 x − h − k to get y = 3 x − 2 − 3 .
The Transformed Function The equation y = 3 x − 2 − 3 represents a cube root function that has been shifted 2 units to the right and 3 units down.
Final Answer Therefore, the transformed function with h = 2 and k = 3 is: y = 3 x − 2 − 3
Examples
Imagine you are designing a water slide. The basic shape of the slide can be modeled by a cube root function. By changing the values of h and k , you can shift the slide left or right ( h ) and up or down ( k ). This allows you to adjust the starting point and height of the slide to fit different landscapes or pool depths. Understanding these transformations helps you customize the slide design without changing its fundamental shape.
