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

To find the equation of the new function after reflecting $f(x)=\log(x)$ over the y-axis, shifting it down 4 units, and shifting it right 1 unit, we need to apply the transformations step by step.<br /><br />Step 1: Reflecting over the y-axis<br />When a function is reflected over the y-axis, the x-coordinate of each point is negated. Therefore, the reflected function is $f(-x)=\log(-x)$.<br /><br />Step 2: Shifting down 4 units<br />To 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: $f(-x)-4=\log(-x)-4$.<br /><br />Step 3: Shifting right 1 unit<br />To shift a function to the right by a certain number of units, we replace $x$ with $(x-\text{number of units})$ in the function. In this case, we want to shift the function to the right by 1 unit, so we replace $x$ with $(x-1)$ in the function: $f(-(x-1))-4=\log(-(x-1))-4$.<br /><br />Therefore, the equation of the new function after applying all the transformations is $g(x)=\log(-(x-1))-4$.<br /><br />Answer: $g(x)=\log(-(x-1))-4$