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What differences do you see between the given function and the parent function? Apply those transformations to the graph of the parent function, g(x)=sqrt(x).
Graph:
Domain: All real numbers.
Range: All real numbers.
The given function is a cube root function.
f(x)= 2sqrt(x)+ 1
The graph of it will be a transformed version of the parent function g(x)=sqrt(x). Cube root functions typically follow the same general format.
f(x)= asqrt(x- h)+ k
To graph the given function, let's show the possible transformations of g(x)=sqrt(x).
| Transformations of g(x) | |
|---|---|
| Vertical Translations | Translation up k units, k>0 y=g(x)+ k |
| Translation down k units, k>0 y=g(x)- k | |
| Horizontal Translations | Translation right h units, h>0 y=g(x- h) |
| Translation left h units, h>0 y=g(x+ h) | |
| Vertical Stretch or Shrink | Vertical stretch, a>1 y= ag(x) |
| Vertical shrink, 0< a<1 y= ag(x) | |
| Reflections | In the x-axis y= -g(x) |
| In the y-axis y=g( -x) | |
Using the table, we can graph the function as a series of transformations. Let's begin with the parent function.
Next, we will multiply the y coordinates by a= 2. This stretches the graph of the parent function by a factor of 2.
Finally, we will translate the graph up 1 unit by adding 1 to each of the y-coordinates.
Looking at the graph of the function, notice that it continues on to infinity in both the positive and negative directions. This means that the domain and range of the function are all real numbers. Domain:& All real numbers. Range:& All real numbers.
