Question

Solve.

5. The graph of f(x)= x is reflected across the x-axis. The graph is then
translated 11 units up and 7 units to the left. Write the equation of the
transformed function.

Answer 1

Given:

The function is:

`f(x)=x`

The graph of this function reflected across the x-axis. The graph is then translated 11 units up and 7 units to the left.

To find:

The equation of the transformed function.

Solution:

The translation is defined as

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

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 is reflected across 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.

The graph of this function reflected across the x-axis. The graph is then translated 11 units up and 7 units to the left. So,
`k=-1, b=11, a=7`. Putting these value in (i), we get

`g(x)=(-1)f(x+7)+11`

`g(x)=-(x+7)+11`
`[\because f(x)=x]`

`g(x)=-x-7+11`

`g(x)=-x+4`

Therefore, the required function is
`g(x)=-x+4`.