Lesson 1 Function Family Reunion Solidify Understanding

Ready

Graph the equations on the corresponding grid.

1.

The graph of $y = x^{2}$ is shown.

a.

Graph the equations on the grid provided.

$y_{1} = x^{2} - 2$
$y_{2} = {(x - 2)}^{2}$
$y_{3} = 2 x^{2}$

b.

For each new equation, explain what the number $2$ does to the graph of $y = x^{2}$ . Identify what changes in the graph and what stays the same. Pay attention to the $y$ -intercept, the $x$ -intercept(s), and the rate of change.

2.

The graph of $y = x^{3}$ is shown.

a.

Graph the equations on the grid provided.

$y_{1} = x^{3} + 3$
$y_{2} = {(x + 3)}^{3}$
$y_{3} = 3 x^{3}$

b.

For each new equation, explain what the number $3$ does to the graph of $y = x^{3}$ . Identify what changes in the graph and what stays the same. Pay attention to the $y$ -intercept, the $x$ -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.

$h (x) = 2^{x}$ , and $j (x) = 2^{- x}$

4.

$r (x) = x^{2}$ , and $s (x) = - \frac{1}{2} x^{2} + 5$

5.

$v (x) = \frac{1}{x}$ , and $w (x) = - \frac{1}{x}$

6.

$k (x) = \log (x)$ ,

and $m (x) = - 1 + \log (x)$

7.

$p (x) = \sin (x)$ ,

and $q (x) = 2 \sin (x + \frac{π}{3})$

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: $f (x) = x^{3}$

	pre-image (parent function)	image 1	image 2
geometric notation	$(x, y)$	$(x, y) \to$ $(x, \underset{―}{})$	$(x, y) \to$ $(\underset{―}{})$
function notation	$f (x) = x^{3}$	$f_{1} (x) =$ $\underset{―}{}$	$f_{2} (x) =$ $\underset{―}{}$
selected points that fit this image	$(- 2, - 8)$	$(- 2, - 3)$	$(- 4, - 8)$
	$(- 1, - 1)$	$(- 1, 4)$	$(- 3, 1)$
	$(0, 0)$	$(0, 5)$	$(- 2, 0)$
	$(1, 1)$	$(1, 6)$	$(- 1, - 1)$
	$(2, 8)$	$(2, 13)$	$(0, - 8)$