1. Warmup Identify the type of function represented by the graph.
A. linear
B. piecewise-defined
C. absolute value
D. parabolic

2. 2-7 Parent Functions and Transformations
We are family!

3. A family of graphs is a group of graphs that display one or more similar characteristics. The parent graph is the simplest of those type of functions. This is what we use to compare when transformations occur.

4. Identify the type of function represented by the graph.

5. We can take these simplest of parent functions and transform them
We can take these simplest of parent functions and transform them. Transformations may change locations, flip over an axis, or stretch or compress.
A translation moves a figure up, down, left or right. It maintains the same shape!
When a constant h is added to or subtracted from x before evaluating a parent function, the result is a translation of the f(x) function left or right. It would be written 𝑓(𝑥±ℎ).

6. 19. Graph 𝑦= 𝑥 and compare to 𝑦= 𝑥+6 . Describe the translation.

7. When a constant k is added to or subtracted from a parent function, the result is a translation of the f(x) function up or down. It would be written 𝑓 𝑥 ±𝑘
38. Write an equation for the function

8. 21. Graph y = x2 and compare to
A reflection flips a figure over a line called the line of reflection. (same size and shape, just mirror image)
When f(x) is multiplied by -1, the result –f(x) is a reflection across the x-axis. (flips vertically)
21. Graph y = x2 and compare to
y = – x2 . Describe the reflection in the function.

9. When only the variable is multiplied by -1, the result f(– x) is a reflection across the y-axis. (flips horizontally)
23. Graph 𝑦= 𝑥 and compare to 𝑦= −𝑥 . Describe the reflection in the function.

10. A dilation shrinks or stretches a figure proportionally.
If a linear function, the slope changes.
If a nonlinear function is multiplied by a nonzero number, it is stretched or shrunk.
Coefficients greater than 1 stretch, and coefficients between 0 and 1 shrink.
30. Graph y = x and compare to y = 2/3 x. Describe the dilation in the function.