Lesson 6 Getting Down to Business Solidify Understanding

Ready

Write the explicit equations for the tables and graphs.

1.

$x$	$f (x)$
$2$ $3$ $4$ $5$	$- 4$ $- 11$ $- 18$ $- 25$

$x$

$f (x)$

$2$

$3$

$4$

$5$

$- 4$

$- 11$

$- 18$

$- 25$

2.

$x$	$f (x)$
$- 1$ $0$ $1$ $2$	$\frac{2}{5}$ $2$ $10$ $50$

$x$

$f (x)$

$- 1$

$0$

$1$

$2$

$\frac{2}{5}$

$2$

$10$

$50$

3.

$x$	$f (x)$
$2$ $3$ $4$ $5$	$- 24$ $- 48$ $- 96$ $- 192$

$x$

$f (x)$

$2$

$3$

$4$

$5$

$- 24$

$- 48$

$- 96$

$- 192$

4.

$x$	$f (x)$
$- 4$ $- 3$ $- 2$ $- 1$	$81$ $27$ $9$ $3$

$x$

$f (x)$

$- 4$

$- 3$

$- 2$

$- 1$

$81$

$27$

$9$

$3$

5.

6.

7.

8.

9.

Set

10.

The balance in an interest-bearing account is modeled with a continuous function over time. Which of the domain choices is a possibility?

A.

Real numbers greater than $0$

B.

Whole numbers

C.

Integers

D.

Natural numbers

11.

Select the only equation that can be used to model a continuous exponential function.

A.

$f (x) = f (x - 1) \cdot b, f (1) = a$

B.

$g (x) = a b^{x - 1}$

C.

$h (x) = m x + b$

D.

$k (n) = k (n - 1) + m, k (0) = b$

12.

Select the only equation type that can be used to model a continuous linear function.

A.

$f (x) = f (x - 1) \cdot b, f (1) = a$

B.

$g (x) = a b^{x - 1}$

C.

$h (t) = m x + b$

D.

$k (n) = k (n - 1) + m, k (0) = b$

13.

The domains of arithmetic and geometric sequences are always subsets of which set of numbers?

A.

Real numbers

B.

Rational numbers

C.

Integers

14.

Select the attributes that characterize both arithmetic and geometric sequences. Select all that apply.

A.

Continuous

B.

Discrete

C.

Domain: ${x | x \in N}$

D.

Domain: ${x | x \in R}$

E.

Negative $x$ -values

F.

Something constant or consistent

G.

Recursive rule

15.

Explain why arithmetic sequences are a subset of linear functions. What makes them different?

16.

Explain why geometric sequences are a subset of exponential functions. What makes them different?

17.

The equation $y = - 4 x + 32$ has many solutions. Some of them are: $(0, 32)$ , $(3, 20)$ , and $(5, 12)$ . How can this equation be represented to show all possible solutions for the equation? Explain how the representation shows all solutions.

18.

The equation $y = 5 {(2)}^{x}$ has many solutions. Some of them are: $(0, 5)$ , $(2, 20)$ , and $(- 1, 2.5)$ . How can this equation be represented to show all possible solutions for the equation? Explain how the representation shows all solutions.

Go

In problems 19 and 21 the first and fifth terms of both an arithmetic and a geometric sequence are given. Find the missing values for each sequence. Then write the explicit equation for each function.

19.

Arithmetic	$3$				$48$
Geometric	$3$				$48$

Arithmetic:

Geometric:

20.

Label the coordinates of the intersection points in the graph based on the table of values given in problem 19.

21.

Arithmetic	$- 12$				$- 0.75$
Geometric	$- 12$				$- 0.75$

Arithmetic:

Geometric:

22.

Label the coordinates of the intersection points in the graph based on the table of values given in problem 21.