Instructions
Complete the exercises below focusing on shifts, stretches, and compressions of linear functions. Show your work where necessary.
1. Understanding Shifts
Identify whether the following linear functions are shifted left, right, up, or down from the parent function f(x) = x. Explain your reasoning in the space provided.
a. g(x) = x + 3
b. h(x) = x - 5
c. j(x) = 2 + x
2. Recognizing Stretches and Compressions
Determine whether the following functions represent a vertical stretch, vertical compression, or neither. Explain your reasoning.
a. k(x) = 3x
b. m(x) = 0.5x
c. n(x) = 2(x - 1)
3. Graphing Challenge
Sketch the graph of the function p(x) = 2(x - 2) + 1 on the graph below. Label key points and show how it is transformed from the parent function.
4. Application Task
Write a short paragraph about a real-world situation in which you might use shifts, stretches, or compressions of linear functions. Explain your ideas clearly.