Find g(x), where g(x) is the translation 3 units right and 11 units up of f(x)= – 3|x–7|–9.

Answer 1

Hi Teresa,

Lets begin by taking f(x) apart to better understand what part does what.

f(x) = -3|x-7|-9

The part x-7 describes were a line with lay relative to the x axis. So in this case -7 means that it will center on 7 on +x axis. The -9 is where the line will intercept along the y axis. In this case the number is negative so it means it will be in either the 3rd or 4th quadrant.

The question says g(x) will be 3 units right and 11 units up from f(x).

We know that the negative numbers along the x axis means go to the right. For g(x) that means |x-10| and it wants to translate up the y axis by 11. Add 11 to -9 we get the y as 2.

Putting all this together the final answer is: g(x) = -3|x-10|+2