Math Problem Statement

Draw a graph of the function y=1/3f(x-3)-5

Solution

The function given is y=13f(x3)5y = \frac{1}{3} f(x - 3) - 5, which represents a transformed version of a function f(x)f(x). The transformation consists of:

  1. Horizontal Shift: x3x - 3 shifts the graph 3 units to the right.
  2. Vertical Scaling: The factor 13\frac{1}{3} compresses the graph vertically by a factor of 3.
  3. Vertical Shift: The 5-5 moves the entire graph down by 5 units.

To draw the graph, I would need more details about the specific function f(x)f(x). If f(x)f(x) is not defined, I can draw a general sketch based on the transformations of any standard function. Should I proceed with a specific type of function, like f(x)=x2f(x) = x^2 (parabola), or do you have another function in mind?

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Math Problem Analysis

Mathematical Concepts

Function Transformations
Horizontal Shift
Vertical Scaling
Vertical Shift

Formulas

y = (1/3)f(x - 3) - 5

Theorems

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Suitable Grade Level

Grades 9-11