Based on the results of Exercises, sketch the graph of f(x) = (x + 2)2 − 1 without using a...

Based on the results of Exercises, sketch the graph of f(x) = (x + 2)2 − 1 without using a graphing calculator. Check your result with a graphing calculator.

Exercises

Let f(x) = x2 . Graph the functions f(x + 1), f(x − 1), f(x + 2), and f(x − 2). Make a guess about the relationship between the graph of a general function f(x) and the graph of f(g(x)), where g(x) = x + a for some constant a. Test your guess on the functions f(x) = x3 and

f(x) =

Shifting a Graph Let f(x) = x2 . Graph the functions f(x) + 1, f(x) − 1, f(x) + 2, and f(x) − 2. Make a guess about the relationship between the graph of a general function f(x) and the graph of f(x) + c for some constant c. Test your guess on the functions f(x) = x3 and

f(x) =