(a) Use the drop-down menu to select the absolute value (x) function. The basic function f (x) =|x| is drawn in a dashed-blue line with three key points labeled. Now, use the slider labeled k to slowly increase the value of k from 0 to 3. As you do this, notice the form of the function g(x) = f (x − h) + k labeled in green. Repeat this for other functions available in the drop-down menu. Based on what you observe, conclude if a positive real number k is added to the outputs of a function y = f (x), the graph of the new function g( x) = f ( x) + k is the graph of f shifted________ (horizontally/vertically)_______ (up/down/left/right) k units.

(b) Use the drop-down menu to select the square root (√x) function. The basic function f (x) =√x is drawn in a dashed-blue line with three key points labeled. Now, use the slider labeled k to slowly decrease the value of k from 0 to −3. As you do this, notice the form of the function g( x) = f (x − h) + k labeled in green. Repeat this for other functions available in the drop-down menu. Based on what you observe, conclude if a positive real number k is subtracted from the outputs of a function y = f ( x), the graph of the new function g(x) = f (x) − k is the graph of f shifted_______ (horizontally/vertically)________ (up/down/left/right) k units.

(c) If y = f (x) is some function whose graph contains the point (2, 4), the graph of y = f (x) + 2 would contain the point ________. Express your answer as an ordered pair.

(d) If y = f (x) is some function whose graph contains the point (3, 2), the graph of y = f (x) − 7 would contain the point _______. Express your answer as an ordered pair.