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blagie [28]
3 years ago
15

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

Mathematics
1 answer:
MrRa [10]3 years ago
8 0

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

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