In two or more complete sentences, describe the transformation(s) that take place on the parent function f(x) = 3x to obtain the graph of f(x) = 3-x + 1 - 5.

Answer 1

I think you're missing some parentheses here. Should it be f(x)= 3 (-x+1) -5 ? The way you wrote it, the function is equivalent to f(x) = -x-1, which wouldn't have the same parent function.

Assuming the function is f(x)= 3 (-x+1) -5 , from f(x) = 3x:

Note: Always approach transformations with PEMDAS in mind. Start with the stuff in the parentheses, addition and subtraction first, then multiplication and division, then move outside the parentheses. Here are the steps in order:

1. f(x)=3(x+1) moves one unit left from f(x)=3x. (Remember, whatever's added or subtracted to the x does the opposite. So (x+1) moves left one, and (x-1) moves right one.)
2. Still in the parentheses: From f(x)=3(x+1) to f(x)=3(-x+1), that negative in front of the x makes all the x values negative, or "reflects the function over the y-axis" is the mathy way to say it.
3. Now, outside the parentheses: From f(x)=3(-x+1) to f(x)=3(-x+1) -5, since the -5 is OUTSIDE the parentheses, it affects the y values. The function moves down 5 units. (Note the y-intercept moves from (0,3) to (0,-2).)

You can make the answer more concise, maybe making each of the three steps into one sentence.

Protip: If you're not sure how a transformation will work, try graphing each step on desmos.com or your calculator, and figure out what happens to the lines. Or make a table for each transformation and watch what happens to your points.

Good luck!