Narration: Determine the effect of adding a value of k to a function. Does anything special happen when k is negative? Adding a value of k to the function f of x causes the function to translate up vertically, or shift up, k units when k is positive, and to translate down vertically, or shift down, when k is negative.
Animation description: The animation shows a parabola opening up with vertex at the origin. The parabola then translates vertically up when the value of k is positive and down when the value of k is negative. The size of the parabola stays the same. The parabola is given the function notation g of x equals f of x plus k.
Narration: The effect of adding a value of k to the function f of x plus k is the same when f of x is quadratic, exponential and linear. Now observe how this exponential function f of x is translated by adding a value of k. The function translates up vertically k units when k is positive and translates down vertically when k is negative.
Animation description: The animation shows an exponential growth function with horizontal asymptote y = 0. The function then translates vertically up when the value of k is positive and down when the value of k is negative. The size of the function stays the same. The function is given the function notation g of x equals f of x plus k.
Narration: Observe how this linear function f of x is translated by adding a value of k. Again, the function slides up vertically k units when k is positive and slides down vertically when k is negative.
Animation description: The animation shows a linear function with a positive slope intersecting the origin. The function then translates vertically up when the value of k is positive and down when the value of k is negative. The slope of the function stays the same. The function is given the function notation g of x equals f of x plus k.