163k views
2 votes
The graph shows g(x), which is a translation of f(x)=|x|. Write the function rule for g(x).

The graph shows g(x), which is a translation of f(x)=|x|. Write the function rule-example-1
User EyfI
by
7.7k points

1 Answer

5 votes

The original function is f(x) = x.

Three transformations are applied: horizontal compression by a factor of 1/4, translation 8 units down, and reflection across the x-axis.

The resulting function rule for g(x) is: g(x) = - (1/16) * x^2 + 8.

Here's the complete calculation for the function rule of g(x) based on the given graph and transformations:

Original Function:

f(x) = x

Transformation 1: Horizontal Compression by a Factor of 1/4:

This transformation shrinks the graph horizontally by a factor of 4. Mathematically, we can represent this by multiplying x by 1/4: g(x) = f(1/4 * x) = (1/4 * x)^2 = (1/16) * x^2

Transformation 2: Translation 8 Units Down:

This transformation shifts the entire graph 8 units downward. We can achieve this by subtracting 8 from the function: g(x) = (1/16) * x^2 - 8

Transformation 3: Reflection across the x-axis:

This transformation flips the graph upside down. We can represent this by multiplying the function by -1: g(x) = -[(1/16) * x^2 - 8] = -(1/16) * x^2 + 8

Therefore, the complete function rule for g(x) after all the transformations is:

g(x) = - (1/16) * x^2 + 8

User Sbleon
by
8.9k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories