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

160

step-by-step explanation:

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