Lesson 7 More Variation Practice Understanding

Ready

In an experiment, an event is the outcome that we are interested in occurring.

The probability of an event $A$ , written as $P (A)$ , is defined as

$P (A) = \frac{Number of favorable outcomes}{Total number of possible outcomes}$

Answer the following questions.

1.

Each letter of the word “S T A T I S T I C S” is written on a card and placed in a box. A card is randomly selected from the box. Find the probability of drawing a card containing the indicated letter.

a.

b.

c.

2.

You roll a standard $6$ -sided die. What is the probability that you will roll

a.

a prime number?

b.

an even number?

c.

a number greater than $5$ ?

3.

A bag contains $5$ red balls, $7$ green balls, $2$ white balls, and $1$ black ball. A ball is randomly selected from the bag. What is the probability of selecting

a.

a red ball?

b.

a white ball?

c.

a yellow ball?

Set

4.

The graph of $y = \frac{1}{x}$ is given. On the same set of axes, sketch the graph of $y = \frac{k}{x}$ when $k = 10$ and when $k = 20$ .

5.

What do the different values of $k$ do to the shape of the graph? Did the location of the asymptotes change?

6.

State the domain of $y = \frac{1}{x}$ . Did the domain and/or range change when $K$ changed? Explain.

7.

Sketch the graph of $y = \frac{1}{x - 6}$ . Describe the change in the graph and the asymptotes.

8.

Sketch the graph of $y = \frac{1}{x} - 6$ . Describe the change in the graph and in the asymptotes.

9.

What is the solution to the equation $f (x) = g (x)$ defined by the system: $[\begin{matrix} f (x) = \frac{1}{x} \\ g (x) = \sqrt{x} \end{matrix}$ ?

10.

Find the solution to the equation $f (x) = g (x)$ defined by the system: $[\begin{matrix} f (x) = \frac{1}{x - 3} \\ g (x) = \frac{2}{x + 3} \end{matrix}$

Go

Identify the type of function in each table. Justify your answer.

Choices for types of functions: linear but not direct variation, linear and direct variation, inverse variation, quadratic, and exponential.

11.

$x$	$y$
$1$	$7$
$2$	$13$
$3$	$23$
$4$	$37$
$5$	$55$

12.

$x$	$y$
$6$	$96$
$7$	$48$
$8$	$24$
$9$	$12$
$10$	$6$

13.

$x$	$y$
$- 4$	$- 28$
$- 6$	$- 42$
$- 8$	$- 56$
$- 10$	$- 70$
$- 12$	$- 84$

14.

$x$	$y$
$2$	$60$
$3$	$40$
$4$	$30$
$5$	$24$
$6$	$20$

15.

$x$	$y$
$11$	$18$
$12$	$21$
$13$	$24$
$14$	$27$
$15$	$30$

16.

$x$	$y$
$3$	$3$
$9$	$1$
$18$	$\frac{1}{2}$
$27$	$\frac{1}{3}$
$36$	$\frac{1}{4}$