Lesson 4 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

The first and fifth terms of a sequence are given. Fill in the missing numbers if it is an arithmetic sequence. Then fill in the numbers if it is a geometric sequence. Write the explicit rule for each function.

Arithmetic: $f (n) = 4 + 80 (n - 1)$

Geometric: $f (n) = 4 {(3)}^{n - 1}$

19.

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

Arithmetic:

Geometric:

20.

Arithmetic	$-6,250$				$- 10$
Geometric	$-6,250$				$- 10$

Arithmetic:

Geometric:

21.

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

Arithmetic:

Geometric: