Math Problem Statement

Fungsi F(x) = 2^x digeser 6 satuan ke kanan. Persamaan Fungsi baru setelah translasi adalah:

Solution

The text in the image is written in Indonesian and can be translated as follows:

"The function F(x)=2xF(x) = 2^x is shifted 6 units to the right. The equation of the new function after the translation is:"

Given the information:

  • The original function is F(x)=2xF(x) = 2^x.
  • The function is shifted 6 units to the right.

To find the new function after a horizontal shift, we use the transformation rule for functions:

F(xh)F(x - h)

Where hh is the horizontal shift. If the shift is to the right, hh is positive. So, in this case, the new function G(x)G(x) after shifting F(x)=2xF(x) = 2^x 6 units to the right is:

G(x)=2(x6)G(x) = 2^{(x - 6)}

So, the equation of the new function is:

G(x)=2x6G(x) = 2^{x-6}

Would you like more details on this or have any questions?

Here are some related questions:

  1. What is the effect of shifting a function vertically versus horizontally?
  2. How does the base of the exponential function affect its graph?
  3. What happens to the graph of F(x)=2xF(x) = 2^x if it is shifted to the left instead?
  4. How would the function change if instead of shifting, it was reflected over the x-axis?
  5. Can you generalize how to transform any function given different types of shifts and reflections?

Tip: When shifting functions horizontally, remember that moving to the right involves subtracting from the input variable, and moving to the left involves adding to it.

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Math Problem Analysis

Mathematical Concepts

Functions
Exponential Functions
Function Transformation

Formulas

F(x - h) = f(x) shifted h units to the right
Exponential Function: F(x) = a^x

Theorems

Transformation of Functions

Suitable Grade Level

Grades 9-12