Math Problem Statement

Analyze the function f(x) = 3√(2x - 1) - 1 and complete the provided worksheet, including graphing the function, determining the domain, range, intercepts, behavior, parent function, transformations, and intervals of increase and decrease.

Solution

The uploaded image appears to involve analyzing and transforming a function of the form f(x)=32x11f(x) = 3 \sqrt{2x - 1} - 1. There is a blank grid in the center for graphing, and several boxes asking for details about the function, such as:

  1. Domain: The set of values xx for which the function is defined.
  2. Range: The set of values that the function can take.
  3. Intercepts: Where the function crosses the x-axis (x-intercept) and y-axis (y-intercept).
  4. Behavior: Including increasing or decreasing intervals.
  5. Parent Function: The basic function that this is derived from.
  6. Transformations: Any shifts, stretches, or compressions applied to the parent function.

Let's analyze the function step by step:

1. Parent Function:

The parent function is f(x)=xf(x) = \sqrt{x}.

2. Transformations:

  • The function is multiplied by 3,

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Math Problem Analysis

Mathematical Concepts

Functions
Square Root Functions
Transformations
Graphing

Formulas

f(x) = 3√(2x - 1) - 1
Parent function: f(x) = √x

Theorems

Function Transformations
Domain and Range of Functions

Suitable Grade Level

Grades 10-12