Question

Describe the 2 transformations that occur when the graph of f(x) =x −−√ is transformed to the graph of g(x) = 2x√ +3 .

Answer 1

Answer:

Dilation followed by Translation.

Step-by-step explanation:

We have the function $f(x)=\sqrt{x}$.

The new transformed function is $g(x)=2\sqrt{x}+3$

Now, the transformation applied to f(x) to obtain g(x) are:

1. Dilation - it is the transformation that changes the size/shape of the figure. It is generally of the form kf(x) where k is constant.

Since, we are dilating the given function by 2 units, the new dilated function becomes $2\sqrt{x}$.

2. Translation - it is the transformation that shifts the figure in any direction. When the function is shifted vertically, the general form becomes f(x)+k.

As, we see that the new dilated function is shifted 3 units upwards, the final translated function becomes $g(x)=2\sqrt{x}+3$.

Hence, the transformations applied to obtain g(x) from f(x) are Dilation followed by Translation.