Lesson 1 Scott’s March Motivation Develop Understanding

Ready

For each problem, place the appropriate inequality symbol between the two expressions to make the statement true.

1.

If $a > b$ , then:

$3 a$ $3 b$

2.

If $a > b$ , then:

$b - a$ $a - b$

3.

If $a > b$ , then:

$a + x$ $b + x$

4.

If $x > 10$ , then:

$x^{2}$ $2^{x}$

5.

If $x > 10$ , then:

$\sqrt{x}$ $x^{2}$

6.

If $x > 10$ , then:

$x^{2}$ $x^{3}$

7.

If $0 < x < 1$ , then:

$x$ $x^{2}$

8.

If $0 < x < 1$ , then:

$\sqrt{x}$ $x$

9.

If $0 < x < 1$ , then:

$x$ $\frac{1}{x}$

Set

For problems 10–12, the recursive rule for a polynomial function is given in the form $f (n) = f (n - 1) + (rate of change)$ .

Use the recursive rule to fill in the first 5 values of the function in the table of values.
Identify the rate of change.
Classify the type of polynomial function as linear, quadratic, or cubic.
Use the differences in the table to check your answer.

10.

$f (1) = 10; f (n) = f (n - 1) + 7$

rate of change:

type of polynomial:

Input	Output
$1$
$2$
$3$
$4$
$5$

11.

$f (1) = - 3; f (n) = f (n - 1) + 2 n$

rate of change:

type of polynomial:

Input	Output
$1$
$2$
$3$
$4$
$5$

12.

$f (1) = 1; f (n) = f (n - 1) + (n^{2} + 3)$

rate of change:

type of polynomial:

Input	Output
$1$
$2$
$3$
$4$
$5$

For problems 13–16,

Find the rate of change for each table of values.
Write the recursive form of each function. If the rate of change is constant, write in the constant value. If the rate of change is a function, write the equation of the function that describes the rate of change.
Identify the type of function.

13.

Input	Output
$0$	$6$
$1$	$7$
$2$	$9$
$3$	$12$
$4$	$16$
$5$	$21$

rate of change:

recursive rule:

type of function:

14.

Input	Output
$1$	$6$
$2$	$1$
$3$	$- 4$
$4$	$- 9$
$5$	$- 14$
$6$	$- 19$

rate of change:

recursive rule:

type of function:

15.

Input	Output
$1$	$3$
$2$	$6$
$3$	$11$
$4$	$18$
$5$	$27$

rate of change:

recursive rule:

type of function:

16.

Input	Output
$1$	$1$
$2$	$5$
$3$	$14$
$4$	$30$
$5$	$55$

rate of change:

recursive rule:

type of function:

Go

Find the quotient without using a calculator. If you have a remainder, write the remainder as a whole number. Example: $\begin{array}{r} 7 \\ 21 149 \end{array}$ r $2$

17.

$30 510$

18.

Is $30$ a factor of $510$ ? How do you know?

19.

Find $3,405 \div 17$ .

20.

Is $17$ a factor of $3,405$ ? How do you know?

21.

$92 3,405$

22.

Is $92$ a factor of $3,405$ ? How do you know?

23.

Subtract: $(7 x^{3} - 11 x^{2} + x - 4) - (5 x^{3} - 9 x + 4)$

24.

Multiply: $(5 x + 1) (- 3 x^{2} - x + 2)$

25.

Multiply: ${(2 x + 5)}^{3}$

26.

The graphs of $f (x)$ and $g (x)$ are given. Create the graph of $f (x) + g (x)$ .