Math Unit 4 Test

Question 1

Multiplication:

Answer 1

When the bases are the same, keep the BASE and ADD the EXPONENT

Question 2

Division:

Answer 2

When the bases are the same, keep the BASE and SUBTRACT the EXPONENT

Question 3

Power of a Power:

Answer 3

Keep the BASE and MULTIPLY the EXPONENTS

Question 4

Zero as an Exponent:

Answer 4

When an exponent is ZERO, the value of the power is 1

Question 5

Negative Exponents:

Answer 5

A negative exponent is the RECIPROCAL of the base with a positive exponent

Question 6

Power of a Product:

Answer 6

When there is more than one base being multiplied together and raised to a power, the exponent is applied to everything inside the bracket

Question 7

Power of a Quotient:

Answer 7

When there is more than one base being divided and raised to a power, the exponent is applied to everything inside the bracket

Question 8

Rational Exponents Definition:

Answer 8

A power with a FRACTION in the exponent

Question 9

The denominator of the exponent tells you the ? of the radical

Answer 9

INDEX

Question 10

When you have a question that contains a mix of radical and exponent forms, it is often beneficial to…

Answer 10

convert everything to exponent form in order to make use of exponent laws to simplify

Question 11

Exponential Equations Rule:

Answer 11

When you have a variable in the exponent, make the bases the same, then set the exponents equal to each other and solve

Question 12

Exponential graphs are of the form

Answer 12

y=ab^x

Question 13

The ‘a’ refers to the

Answer 13

vertical stretch/compression (the same as the previous units)

Question 14

If a is a negative, there’s

Answer 14

a reflection in the x axis

Question 15

Parent function y=2^x

Answer 15

(-1,½) (0,1) (1,2) (2,4) (3,8)
Y-int: 1
a=1, b=2
Increasing
Domain: {xER}, Range: {yER|y>0}

Question 16

Parent function y=3^x

Answer 16

(-1,⅓ ) (0,1) (1,3) (2,9) (3,27)
Y int: 1
a=1, b=3
Increasing
Domain: {xER}, Range: {yER|y>0}

Question 17

Parent function= ½ ^x

Answer 17

(-1,2) (0,1) (1,½) (2,¼) (3,⅛)
Y-int: 1
a=1, b=½
Decreasing
Domain: {xER}, Range: {yER|y>0}

Question 18

Parent function= ⅓ ^x

Answer 18

(-1,3) (0,1) (1,⅓ ) (2,1/9) (3,1/27)
Y-int: 1
a=1, b=⅓
Decreasing
Domain: {xER}, Range: {yER|y>0}

Question 19

All graphs have the ordered pair (0,1) when the ‘a’ value is

Answer 19

1

Question 20

When b＞1

Answer 20

the graph increases and becomes steeper as b gets higher

Question 21

When b is a fraction,

Answer 21

the graph decreases

Question 22

To figure out any points

Answer 22

use (-1, 0, 1, 2 ,3) as the x’s and make the y for -1 a fraction, 0 is 1, 1 is whatever the number is, and then multiple by b to keep going up

Question 23

In y=af[k(x-d)] + c, a is..

Answer 23

Direction of Opening (reflection of x axis)
Vertical Stretch/Compression

Question 24

In y=af[k(x-d)] + c, k is..

Answer 24

Reflection of y axis
Horizontal Stretch/Compression

Question 25

In y=af[k(x-d)] + c, d is..

Answer 25

Horizontal translation left/right

Question 26

In y=af[k(x-d)] + c, c is..

Answer 26

Vertical translation up/down

Question 27

Asymptote:

Answer 27

a line that a curve approaches but never crosses, as it heads towards infinity

Question 28

Increasing:

Answer 28

y- values get bigger as you move from left to right

Question 29

Decreasing:

Answer 29

y- values get smaller as you move from left to right

Question 30

Steps for Graphing:

Answer 30

Graph the Parent Function, create a Table of Values with a minimum of 4 points
Use Mapping Notation to do the Transformations given by In y=af[k(x-d)] + c
Graph the translated graph

Question 31

Exponential function form:

Answer 31

y=ab^k(x-d)+c

Question 32

Mapping Notation:

Answer 32

(1/kx +d, ay+c)

Question 33

The asymptote changes depending on the ? value

Answer 33

c

Question 34

When c = -1, y = ?

Answer 34

-1

Question 35

Remember to factor out the ? value

Answer 35

k

Question 36

Rates of Increase/Decrease (‘b’ value)
For half-life

Answer 36

b=½

Question 37

Rates of Increase/Decrease (‘b’ value)
For doubling, tripling,…

Answer 37

:b=2, b=3..

Question 38

Rates of Increase/Decrease (‘b’ value)
For appreciation:

Answer 38

b = 1 + percent/100

Question 39

Rates of Increase/Decrease (‘b’ value)
For depreciation:

Answer 39

b = 1 - percent/100

Question 40

In y = ab^x

Answer 40

Y = result or future value
A = initial value (y intercept)
B = Rate of increase/decrease ratio
X = Number of times if has grown/decayed

Question 41

In y = ab^x/xn

Answer 41

X = total time
Xn = Time it takes to grow/decay