Problemas
If f(x)=log(x) is reflected over the y-axis, shifted down 4 units, and shifted right I unit, then what equation below represents this new function? I g(x)=log(-x+4)-1 I g(x)=log(x+1)-4 D g(x)=-log(x-1)-4 g(x)=-log(x+4)-1 g(x)=log(-(x-1))-4
Roztwór
Daniela
professionell · Tutor durante 6 años
4.3
(119 Votos)
Respuesta
To find the equation of the new function after reflecting
over the y-axis, shifting it down 4 units, and shifting it right 1 unit, we need to apply the transformations step by step.Step 1: Reflecting over the y-axisWhen a function is reflected over the y-axis, the x-coordinate of each point is negated. Therefore, the reflected function is
.Step 2: Shifting down 4 unitsTo shift a function down by a certain number of units, we subtract that number from the function. In this case, we want to shift the function down by 4 units, so we subtract 4 from the function:
.Step 3: Shifting right 1 unitTo shift a function to the right by a certain number of units, we replace
with
in the function. In this case, we want to shift the function to the right by 1 unit, so we replace
with
in the function:
.Therefore, the equation of the new function after applying all the transformations is
.Answer: