Respuesta :
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.
A function can be transformed by stretching it and by translating it.
The equation of the transformation is: [tex]y''' = 2|x + 3| -4[/tex]
The parent function is given as:
[tex]y = |x|[/tex]
The rule of vertical stretch by 2 is:
[tex](x,y) \to (x,2y)[/tex]
So, we have:
[tex]y' = 2y[/tex]
Substitute [tex]y = |x|[/tex]
[tex]y' = 2|x|[/tex]
The rule of shifting a function left by 3 units is:
[tex](x,y) \to (x + 3,y)[/tex]
So, we have:
[tex]y'' = 2|x + 3|[/tex]
The rule of shifting a function down by 4 units is:
[tex](x,y) \to (x,y -4)[/tex]
So, we have:
[tex]y''' = 2|x + 3| -4[/tex]
Hence, the resulting function is:
[tex]y''' = 2|x + 3| -4[/tex]
Read more about transformation at:
https://brainly.com/question/13810353
