The given absolute value function is f(x)=∣−3x+61∣+9f(x)=∣−3x+61∣+9.
To determine the horizontal shift for this function, we look at the expression inside the absolute value, which is −3x+61−3x+61. The horizontal shift for an absolute value function is determined by setting the expression inside the absolute value equal to zero and solving for xx.−3x+61=0−3x+61=0
Adding 3x3x to both sides:61=3x61=3x
Dividing by 3:x=613x=361
This tells us that the function is shifted horizontally by 613361 units. Since the coefficient of xx is negative, the shift is to the right. Therefore, the horizontal shift for the given absolute value function is 613361 units to the right.
