Question

Select the function that represents the transformation of the parent function three units to the left and up two.

f(x) = |x - 3| - 2
f(x) = -|x - 3| + 2
f(x) = |x + 3| + 2
f(x) = -|x + 3| + 2

Answer 1

The third.

When you have a number in the parentheses(abs value function in this case) that is applied to the x value of the graph in the negative way. Since the 3 is positive, the graph will move to the left(negative) 3 spaces. Outside of the parentheses is the opposite; since the two is positive, it will move two places up, resulting in C being the only possible answer.

The reason it isn't D is because adding a negative to the front of the function would flip it over an axis which is not something we want to do here.

Answer 2

The correct option is C. f(x) = |x + 3| + 2

Explanation:

The parent function in this case is : mod x = |x|

Let the parent function be f(x) = |x|

Now, The parent function is transformed 3 units to the left

⇒ f (x) = f(x + 3)

⇒ f(x) = |x + 3|

Also, The parent function is transformed up by 2 units

⇒ f(x) = f(x) + 2

⇒ f(x) = |x + 3| + 2

Therefore, The correct option is C. f(x) = |x + 3| + 2