Question

Write an equation of the translated function of the parent function f(x)=|x| with the following transformations:

Answer 1

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 $y = f (\frac{1}{4}x)$

This operation horizontally expands the function f (x) = | x | in a factor of 4 units. $y = |\frac{1}{4}x + 1|$

3. Do $y = f(x)-4$

This operation vertically shifts the function f (x) = | x | by a factor of 4 units down on the y-axis.

$y = |\frac{1}{4}x +1| -4$

4. After these transformations the function f(x) = | x | it looks like:

$f(x) = |\frac{1}{4}x +1| -4$

Therefore the correct option is option b. You can verify that your vertex is at point (-4, -4) by making f (-4)

$f(-4) = |\frac{1}{4}(-4) +1| -4 = -4$