Lesson 11 Music to My Ears Practice Understanding

Ready

1.

$f (x) = x^{5}$

$x$	$f (x)$
$0$
$1$
$2$
$3$
$4$
$5$
$6$
$7$

2.

$g (x) = 5^{x}$

$x$	$g (x)$
$0$
$1$
$2$
$3$
$4$
$5$
$6$
$7$

3.

Use the tables to label the graphs as $f (x)$ and $g (x)$ .

4.

Compare the growth of the two functions by discussing the three questions.

Which function is growing the fastest on the interval between $x = 0$ and $x = 5$ ?
What is happening at $x = 5$ ?
Which function eventually exceeds the other?

Set

5.

Marian works as a trainer for dogs. One of the tricks she has the dogs do is run through an obstacle course. As a prize for running the course successfully, she gives them a treat at the end. She is wondering if the type of treat will impact how fast the dogs get through the course. To test this, she randomly separates her $10 dogs$ into $2$ groups of $5$ and times how many seconds it takes to race through the course to get the treat at the end. The results are given below.

Group A

$37$

$39$

$45$

$42$

$40$

Group B

$35$

$43$

$34$

$37$

$39$

Is there convincing evidence the type of treat at the end of the course impacts the times of the dogs? Design and carry out a simulation to answer this question.

Go

6.

Fill in the blanks to complete the definition of the inverse sine function.

The equation $y = \sin^{- 1} x$ means “find the , on the interval , such that $\sin y =$ .”

7.

Sketch a graph of $y = \sin^{- 1} x$ .

8.

Explain why the range of the inverse sine function is $- \frac{π}{2} \leq x \leq \frac{π}{2}$ .

9.

Explain why the range of the inverse cosine function is $[0, π]$ .

10.

Sketch a graph of $y = \cos^{- 1} x$ .

11.

Sketch the graph of $y = \tan x$ . Sketch in your asymptotes with dotted lines.

12.

Sketch a graph of $y = \tan^{- 1} x$ .