Answer:
Option b
Step-by-step explanation:
To write the searched equation we must modify the function f (x) = | x | in the following way:
1. Do y = f(x + 4)
This operation horizontally shifts the function f(x) = | x | by a factor of 4 units to the left on the x axis.
y = | x +4 |
2. Do [tex]y = f (\frac{1}{4}x)[/tex]
This operation horizontally expands the function f (x) = | x | in a factor of 4 units. [tex]y = |\frac{1}{4}x + 1|[/tex]
3. Do [tex]y = f(x)-4[/tex]
This operation vertically shifts the function f (x) = | x | by a factor of 4 units down on the y-axis.
[tex]y = |\frac{1}{4}x +1| -4[/tex]
4. After these transformations the function f(x) = | x | it looks like:
[tex]f(x) = |\frac{1}{4}x +1| -4[/tex]
Therefore the correct option is option b. You can verify that your vertex is at point (-4, -4) by making f (-4)
[tex]f(-4) = |\frac{1}{4}(-4) +1| -4 = -4[/tex]
