Narration: Determine the effect of multiplying a function by different values of k. What happens when k increases? What happens when k decreases? Does anything special happen when k is negative?
Animation description: The animation shows a parabola opening up with vertex at the origin. The parabola then gets very skinny for large values of x and gets very wide for small values of x. The parabola is reflected in the x-axis when k is negative. The parabola is given the function notation g of x equals k times f of x.
Narration: When the function is quadratic or exponential, multiplying by k will dilate, or stretch, the function for large values of k and reduce, or shrink, the function for small, positive values of k. When k is negative, the function is reflected or flipped in the x-axis.
Animation description: The first animation repeats showing a parabola opening up with vertex at the origin. The parabola then gets very skinny for large values of x and gets very wide for small values of x. The parabola is reflected in the x-axis when k is negative. The parabola is given the function notation g of x equals k times f of x.
Narration: For linear functions, multiplying by k will increase the slope of the line for large values of k and decrease the slope of the line for small values of k. When k is negative, the function is also reflected or flipped in the x-axis.
Animation description: The animation shows a linear function with positive slope passing through the origin. The slope of the function increases for large values of x and decreases for small values of x. The function is reflected in the x-axis when k is negative. The function is given the function notation g of x equals k times f of x.