The parent function y = |x| stretched vertically by a factor of 2, shifted left 3 units and down 4 units

whats the equation?

Hello!

Let's go through some formula to distinguish the changes that happen to a graph's equation when they are transformed.

Vertical shifts have this type of formula:

f (x) + k → up k units and f (x) - k → down k units

Horizontal shifts have this type of formula:

f (x + k) → left k units and f (x - k) → right k units

Reflections have this type of formula:

-f (x) → reflect over x-axis and f (-x) → reflect over y-axis

Vertical stretches have this type of formula:

a · f (x) where a > 1

Vertical compressions have this type of formula:

a · f (x) where a < 1

Horizontal stretches have this type of formula:

f (a · x) where a > 1

Horizontal compressions have this type of formula:

f (a · x) where a < 1

With that in mind, we can write our transformed absolute value function.

Since the equation is vertically stretched by a factor of 2, a = 2.

y = 2|x|

Also, since the function is shifted left 3 units, k = - 3.

y = 2|x + 3|

Finally, the function is also shifted down 4 units, so k = - 4.

y = 2|x + 3| - 4

Therefore, the equation is y = 2|x + 3| - 4.