Narration: Adding a value of k to the domain of the function f of x causes the function to translate horizontally, shifting left k units when k is positive and shifting right k units when k is negative. It is the opposite of what you might expect! The effect of adding a value of k to the function f of the quantity x plus k is the same when f of x is quadratic, exponential and linear.
Animation description: The animation shows a parabola opening up with vertex at the origin. The parabola then translates horizontally to the left when the value of k is positive and to the right 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 the quantity x plus k.
Narration: Observe the effect of adding a value of k to the function when f of x is exponential. The function translates horizontally, shifting left k units when k is positive and shifting right k units when k is negative.
Animation description: The animation shows an exponential growth function with horizontal asymptote of y=0. The function then translates horizontally to the left when the value of k is positive and to the right 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 the quantity x plus k.
Narration: Observe the effect of adding a value of k to the function when f of x is linear. Again, the function translates horizontally, shifting left k units when k is positive and shifting right when k is negative.
Animation description: The animation shows a linear function with positive slope passing through the origin. The function then translates horizontally to the left when the value of k is positive and to the right 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 the quantity x plus k.