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?

Accepted Solution

Answer:[tex]f(x)=-2log(3x)+3[/tex]Step-by-step explanation:we have[tex]f(x)=log(3x)[/tex]step 1Reflecting the function f(x) over the x-axiswe know thatTo reflect a function about the x-axis, multiply the function by -1f(x) -----> -f(x)so[tex]f(x)=-log(3x)[/tex]step 2Stretching the function f(x) vertically by a factor of twoTo stretch a function vertically, multiply the function by twof(x) -----> 2f(x)[tex]f(x)=-2log(3x)[/tex]step 3Shifting the function f(x) up three unitsTo shift the function up, adds three units to the functionf(x) -----> f(x) +3 [tex]f(x)=-2log(3x)+3[/tex]