Math Problem Statement

Toolkit Function: f(x) = √x Transformation Description: Left 1 What is the equation for the transformed function?

Solution

To solve the problem of determining the equation for the transformed function when the original function f(x)=xf(x) = \sqrt{x} is shifted left by 1 unit, we need to understand how horizontal shifts affect the function.

Transformation Explanation:

When a function f(x)f(x) is shifted to the left by hh units, the new function can be written as: f(x+h)f(x + h) In this case, since the function is shifted left by 1 unit, the transformed function will be: f(x+1)f(x + 1) Substituting the original function f(x)=xf(x) = \sqrt{x} into this, we get: f(x+1)=x+1f(x + 1) = \sqrt{x + 1}

Final Answer:

The equation for the transformed function is: f(x)=x+1\boxed{f(x) = \sqrt{x + 1}}

Would you like to go into more details or have any questions?

Here are some related questions to explore further:

  1. What is the effect on the graph when the function is shifted right by 1 unit instead?
  2. How does shifting the function up or down affect the equation?
  3. What is the general formula for shifting a function horizontally by any number of units?
  4. How does the domain of x\sqrt{x} change after the transformation?
  5. Can we apply multiple transformations to f(x)f(x)? How would you describe the transformation if the function is shifted left by 1 and down by 2?

Tip: When shifting functions horizontally, the direction of the shift is opposite the sign inside the function's argument.

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Math Problem Analysis

Mathematical Concepts

Function Transformation
Square Root Function

Formulas

f(x + h) represents a horizontal shift by h units

Theorems

Function Transformation Theorem

Suitable Grade Level

Grades 9-10