Question

In two or more complete sentences, identify the parent function, and describe the transformations that were applied to
obtain the graph, f(x) - 2x + 6-3

Answer 1

The parental function is $y=\sqrt{x}$ and to obtain the equation $y = \sqrt{2x+6}-3$ we must first resize it (multiply x by 2), then move it 6 units to the left (2x + 6) and after all, go 3 units down with the graph

Answer 2

The parent function is $f(x)=\sqrt{x}$

What is parent function ?

A parent function represents the collection of some functions, i.e. family of functions. It is the simplest form of a family of functions.

A parent function always maintain the same highest degree and the same shape in graph with family of the parent function.

What is the required parent function ?

The required parent function is $f(x)=\sqrt{x}$   i.e. $y=\sqrt{x}$

What are the required transformations ?

To get the given equation f(x) = $\sqrt{2x+6}-3$

We first multiply 2 with x, we get f(x) = $\sqrt{2x}$

Then we move this 6 units to the left, we get f(x) = $\sqrt{2x+6}$

Now, We have to go 3 units downwards, then f(x) = $\sqrt{2x+6}-3$

Hence the given equation.

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