1. 1.4 Shifts, Reflections, and Stretches

2. 6 Common parent functions Constantlinear absolute value Quadraticcubic square root

3. Vertical and horizontal shifts The following changes in the functions y=f(x) will produce the stated shifts in the graph of y=f(x): H(x)=f(x-c)horizontal shift c units to the right H(x)=f(x+c)horizontal shift c units to the left H(x)=f(x)-cvertical shift c units downward H(x)=f(x)+cvertical shift c units upward

4. Describing shifts Describe the shifts of generated by the following

5. Answer Vertical shift down one unit Horizontal shift right one unit Horizontal shift left two units and vertical shift up one unit

6. Reflections The following changes in the function y=f(x) will produce the stated reflections in the graph of y=f(x): H(x)=-f(x)reflection with respect to the x-axis H(x)=f(-x)reflection with respect to the y-axis

7. Describing reflections Describe the reflections of generated by the following

8. Answer Therefore reflected with respect to the y-axis Therefore reflected with respect to the x-axis

9. Nonrigid transformations Nonrigid transformations actually distort the shape of the graph, instead of just shifting or reflecting it. Nonrigid transformations of y=f(x) come from equations of the form y=cf(x). If c>1, then there is a vertical stretch of the graph of y=f(x). If 0<c<1, then there is a vertical shrink We will discuss horizontal extensions and compressions at a further date.

10. Describing stretches Describe the stretches of generated by the following

11. Answer Because 3 factored out and meant the graph was stretched by 3 in the vertical direction

12. Put it all together Determine all shifts, reflections, and stretches of the absolute value parent function given by the following

13. Answer - (reflect over x-axis) 5 (stretch vertically by 5) +2 (shift horizontally left 2 units) -6 (shift vertically down 6 units)