Question

Which graph is an example of a function whose parent graph is of the form y = √x?

Answer 1

The correct option is 1.

Explanation:

The given parent function is

`y=√(x)`

It is a radical parent function. Portieres of this function are

1. Domain=[0,∞)

2. Range=[0,∞)

3. Graph of this function is a single continuous increasing curve.

4. It Increases at decreasing rate.

In first graph the a continuous curve starts from (-4,-1), and increasing at decreasing rate. So, it is represents the graph of a radical function.

`y=√(x+4)-1`

Therefore graph 1 is an example of a function whose parent graph is of the form y = √x.

Second graph is a U-shaped curve, so it is the graph of a quadratic function.

Third graph is a rectangular hyperbola, so it represents a rational functions.

In fourth graph the function increasing at increasing rate, so it represents an exponential function.

Therefore the correct option is 1.

Answer 2

The correct option is 1.

Explanation:

The given parent function is

`y=√(x)`

1. Domain of the function is all positive real number including 0.

2. Range of the function is all positive real number including 0.

3. It is an increasing function. It increases at decreasing rate.

First graph increase at decreasing rate and it starts from (-4,-1), therefore the required function is

`y=√(x+4)-1`

Therefore graph 1 is an example of a function whose parent graph is of the form y = √x.

Second graph is a parabola, so it is the graph of a quadratic function.

Third graph is a rectangular hyperbola, so it is the graph of a rational functions.

Fourth graph is increasing at increasing rate, so it is the graph of an exponential function.

Therefore options 2, 3 and 4 are incorrect.