Question

The parent function f(x) = log3x has been transformed by reflecting it over the x-axis, stretching it vertically by a factor of two and shifting it up three units. which function is representative of this transformation?

Answer 1

`f(x)=-2log(3x)+3`

Explanation:

we have

`f(x)=log(3x)`

step 1

Reflecting the function f(x) over the x-axis

we know that

To reflect a function about the x-axis, multiply the function by -1

f(x) -----> -f(x)

so

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

step 2

Stretching the function f(x) vertically by a factor of two

To stretch a function vertically, multiply the function by two

f(x) -----> 2f(x)

`f(x)=-2log(3x)`

step 3

Shifting the function f(x) up three units

To shift the function up, adds three units to the function

f(x) -----> f(x) +3

`f(x)=-2log(3x)+3`