Math Problem Statement

Tentukan bentuk fungsi x^2 jika di geser 2 satuan ke kanan dan 1 satuan ke atas.

Solution

The image shows a problem in Indonesian that asks to determine the transformation of the function x2x^2 when it is shifted 2 units to the right and 1 unit up.

The general form for shifting a function is as follows:

  • Shifting horizontally by hh units: f(xh)f(x-h) (to the right) or f(x+h)f(x+h) (to the left).
  • Shifting vertically by kk units: f(x)+kf(x) + k (up) or f(x)kf(x) - k (down).

Given:

  • The function is f(x)=x2f(x) = x^2.
  • A shift 2 units to the right means replacing xx with x2x-2, so the horizontal transformation becomes (x2)2(x-2)^2.
  • A shift 1 unit up means adding 1 to the function, making the vertical transformation (x2)2+1(x-2)^2 + 1.

Thus, the transformed function is: f(x)=(x2)2+1f(x) = (x - 2)^2 + 1

This represents the function x2x^2, shifted 2 units to the right and 1 unit up.

Would you like more details, or do you have any questions?

Here are 5 related questions to practice with:

  1. What is the transformation of x2x^2 if it is shifted 3 units to the left and 4 units down?
  2. How would you write the function x2x^2 if shifted 5 units to the right and 2 units down?
  3. If the function x2x^2 is reflected over the x-axis and then shifted 2 units up, what is the resulting equation?
  4. What happens to the graph of x2x^2 if it is shifted 1 unit to the right and stretched vertically by a factor of 3?
  5. How do you shift the graph of x2x^2 by 2 units left and 3 units up?

Tip: Always apply horizontal transformations before vertical ones when writing shifted functions.

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Math Problem Analysis

Mathematical Concepts

Function Transformations
Quadratic Functions

Formulas

Horizontal shift: f(x - h)
Vertical shift: f(x) + k

Theorems

Transformation of Functions

Suitable Grade Level

Grades 9-10