Analyzing Graph Transformations
Consider the function \(f(x) = |x|\). A new function \(g(x)\) is defined as \(g(x) = 2|x – 3| – 4\). Describe the transformations that map the graph of \(f(x)\) to the graph of \(g(x)\).
Translation of a Piecewise Function
Consider the piecewise function defined by: \( f(x) = \begin{cases} x+1, & x < 0 \\ x^2, & x \ge 0 \end{cases}\). Describe how the graph of the function transforms to form \( g(x) = f(x+2) + 3 \). Make sure to identify the new break point and provide the expressions for each segment of […]
Graph Transformation Identification
Consider a function \(f(x)\) whose graph is provided. Without a calculator, identify the effect of the transformation represented by the function \(g(x) = f(x-3) + 2\). Specifically, describe the changes to the graph of \(f(x)\) in terms of horizontal and vertical shifts.