Lesson 1 Function Family Reunion Solidify Understanding

Ready

Graph the equations on the corresponding grid.

1.

The graph of is shown.

a.

Graph the equations on the grid provided.

a parabola opening up graphed on a coordinate plane x–5–5–5555y–5–5–5555000

b.

For each new equation, explain what the number does to the graph of . Identify what changes in the graph and what stays the same. Pay attention to the -intercept, the -intercept(s), and the rate of change.

2.

The graph of is shown.

a.

Graph the equations on the grid provided.

a cubic function graphed on a coordinate plane x–5–5–5555y–5–5–5555000

b.

For each new equation, explain what the number does to the graph of . Identify what changes in the graph and what stays the same. Pay attention to the -intercept, the -intercept(s), and the rate of change.

Set

Sketch the graph of the parent function and the graph of the transformed function on the same set of axes.

3.

, and

a blank 17 by 17 grid

4.

, and

a blank 17 by 17 grid

5.

, and

a blank 17 by 17 grid

6.

,

and

a blank coordinate plane 222444666–2–2–2222000

7.

,

and

a blank coordinate plane x–π–π–π–2π / 3–2π / 3–2π / 3–π / 3–π / 3–π / 3π / 3π / 3π / 32π / 32π / 32π / 3πππy–2–2–2222000

8.

Use the graph and the table to write the rule for each of the different transformations of the parent graph represented in the columns labeled image 1 and image 2. Write the transformation rule as a geometric transformation of the original image, using the set of coordinate points, and then write the rule using algebraic function notation. Graph image 1 and image 2 on the same set of axes. (It’s possible that not all of the transformed points will fit on the given set of axes.)

Graph of parent function:

a cubic function graphed on a coordinate plane x–5–5–5555y–40–40–40–20–20–20202020404040000

pre-image

(parent function)

image 1

image 2

geometric notation

function notation

selected points that

fit this image

Go

Find the function values: , , and . Indicate if the function is undefined for a given value of .

9.

a.

b.

c.

10.

a.

b.

c.

11.

a.

b.

c.

12.

a.

b.

c.

13.

a.

b.

c.

14.

a.

b.

c.

15.

a.

b.

c.

16.

a.

b.

c.

17.

a.

b.

c.

18.

a.

b.

c.

19.

a.

b.

c.

20.

a.

b.

c.