Linear Transformations

1. Given the graph of \(f(x)=\sqrt x \). Describe the transformations that occur in the following graphs of \(g(x)\).   solution

 (a) \(g(x) = \sqrt{x} + 2 \)      (b) \(g(x) = \sqrt{x+2} -1 \)     (c) \(g(x) = -\sqrt{x} +5 \)     (d) \(g(x) = \sqrt{-x} + 3 \)

 2. Given the graph of \(f(x)=|x| \). Describe the transformations that occur in the following graphs of \(g(x)\).   solution

(a) \(g(x) = |x-2| \)          (b) \(g(x) = |x+3| + 5 \)       (c) \(g(x) = |x-1| - 2 \)               (d) \(g(x) = - |x+2| + 3 \)

 3. If the graph of \(\displaystyle{f(x) = x^2}\) is shifted 3 units to the right and 2 units down, what is the equation of the new graph?   solution

4. If the graph of \(\displaystyle{f(x) = \sqrt x}\) is shifted 5 units to the left and 4 units up, what is the equation of the new graph?   solution

5. The graph below is  the function \(y=f(x)\). On the same axis, draw the graph the graph of \(y = f(x-2) + 1\).   solution

6. The graph below is  the function \(y=f(x)\). On the same axis, draw the graph the graph of \(y =  f(-x) - 2 \).   solution