Question

Please help me!!....

Answer 1

Given:

The parent function is

`f(x)=x^2`

The graphs of f(x) and g(x) are given.

To find:

The function g(x).

Solution:

From the given graph it is clear that the graph of f(x) is reflected over the x-axis and shifted 3 units down to get the graph of g(x).

The translation is defined as

`g(x)=kf(x+a)+b` .... (1)

Where, k is stretch factor, a is horizontal shift and b is vertical shift.

If 0<k<1, then the graph compressed vertically by factor k and if k>1, then the graph stretch vertically by factor k. If k<0, then the graph of f(x) reflected over the x-axis.

If a>0, then the graph shifts a units left and if a<0, then the graph shifts a units right.

If b>0, then the graph shifts b units up and if b<0, then the graph shifts b units down.

From the given graph it is clear that the graph of f(x) is reflected over the x-axis and shifted 3 units down to get the graph of g(x). So, k=-1, a=0 and b=-3.

`g(x)=(-1)f(x+0)+(-3)`

`g(x)=-f(x)-3`

`g(x)=-x^2-3`
`[\because f(x)=x^2]`

Therefore, the required function is
`g(x)=-x^2-3`. So, the correct option is B.