Lesson 2 You Are the Imagineer Develop Understanding

Ready

1.

The black curve in the graph shows the graph of $f (x) = \sin (x)$ .

a.

Write the equation of the green dotted line labeled $g (x)$ .

b.

Write the equation of the purple dotted line labeled $h (x)$ .

c.

List everything you notice about the graphs of $f (x)$ , $g (x)$ , and $h (x)$ .

2.

The black curve in the graph shows the graph of $f (x) = \sin (x)$ .

a.

Write the equation of the purple line labeled $m (x)$ .

b.

Sketch in the graph of $f (x) \cdot m (x)$ .

c.

What is the equation of $f (x) \cdot m (x)$ ?

d.

Would the line $y = - 3$ also be a boundary line for your sketch? Explain.

3.

The black curve in the graph shows the graph of $f (x) = \sin (x)$ .

a.

Write the equation of the purple line labeled $b (x)$ .

b.

Sketch in the graph of $f (x) \cdot b (x)$ .

c.

What is the equation of $f (x) \cdot b (x)$ ?

d.

How is the graph of $f (x) \cdot b (x)$ different from the graph of $f (x) \cdot m (x)$ ?

e.

Would the line $y = 3$ also be a boundary line for your sketch? Explain.

Set

4.

$f (x) = x$

$g (x) = \sin (x)$

$h (x) = f (x) + g (x)$

a.

Fill in the values for $h (x)$ in the table.

$x$	$f (x)$	$g (x)$
$- 2 π$	$- 6.28$	$0$
$- \frac{3 π}{2}$	$- 4.71$	$1$
$- π$	$- 3.14$	$0$
$- \frac{π}{2}$	$- 1.57$	$- 1$
$0$	$0$	$0$
$\frac{π}{2}$	$1.57$	$1$
$π$	$3.14$	$0$
$\frac{3 π}{2}$	$4.71$	$- 1$
$2 π$	$6.28$	$0$

b.

With a smooth curve, graph

$h (x) = x + \sin (x)$

5.

$f (x) = x$

$g (x) = \sin (x)$

$k (x) = f (x) \cdot g (x)$ or $k (x) = x \cdot \sin (x)$

a.

Fill in the values for $k (x)$ in the table.

$x$	$f (x)$	$g (x)$
$- 2 π$	$- 6.28$	$0$
$- \frac{3 π}{2}$	$- 4.71$	$1$
$- π$	$- 3.14$	$0$
$- \frac{π}{2}$	$- 1.57$	$- 1$
$0$	$0$	$0$
$\frac{π}{2}$	$1.57$	$1$
$π$	$3.14$	$0$
$\frac{3 π}{2}$	$4.71$	$- 1$
$2 π$	$6.28$	$0$

b.

Now graph $k (x) = f (x) \cdot g (x)$

$k (x) = x \cdot \sin (x)$ .