Math Unit 4 Test Flashcards
Multiplication:
When the bases are the same, keep the BASE and ADD the EXPONENT
Division:
When the bases are the same, keep the BASE and SUBTRACT the EXPONENT
Power of a Power:
Keep the BASE and MULTIPLY the EXPONENTS
Zero as an Exponent:
When an exponent is ZERO, the value of the power is 1
Negative Exponents:
A negative exponent is the RECIPROCAL of the base with a positive exponent
Power of a Product:
When there is more than one base being multiplied together and raised to a power, the exponent is applied to everything inside the bracket
Power of a Quotient:
When there is more than one base being divided and raised to a power, the exponent is applied to everything inside the bracket
Rational Exponents Definition:
A power with a FRACTION in the exponent
The denominator of the exponent tells you the ? of the radical
INDEX
When you have a question that contains a mix of radical and exponent forms, it is often beneficial to…
convert everything to exponent form in order to make use of exponent laws to simplify
Exponential Equations Rule:
When you have a variable in the exponent, make the bases the same, then set the exponents equal to each other and solve
Exponential graphs are of the form
y=ab^x
The ‘a’ refers to the
vertical stretch/compression (the same as the previous units)
If a is a negative, there’s
a reflection in the x axis
Parent function y=2^x
(-1,½) (0,1) (1,2) (2,4) (3,8)
Y-int: 1
a=1, b=2
Increasing
Domain: {xER}, Range: {yER|y>0}
Parent function y=3^x
(-1,⅓ ) (0,1) (1,3) (2,9) (3,27)
Y int: 1
a=1, b=3
Increasing
Domain: {xER}, Range: {yER|y>0}
Parent function= ½ ^x
(-1,2) (0,1) (1,½) (2,¼) (3,⅛)
Y-int: 1
a=1, b=½
Decreasing
Domain: {xER}, Range: {yER|y>0}
Parent function= ⅓ ^x
(-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}
All graphs have the ordered pair (0,1) when the ‘a’ value is
1
When b＞1
the graph increases and becomes steeper as b gets higher
When b is a fraction,
the graph decreases
To figure out any points
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
In y=af[k(x-d)] + c, a is..
Direction of Opening (reflection of x axis)
Vertical Stretch/Compression
In y=af[k(x-d)] + c, k is..
Reflection of y axis
Horizontal Stretch/Compression
In y=af[k(x-d)] + c, d is..
Horizontal translation left/right
In y=af[k(x-d)] + c, c is..
Vertical translation up/down
Asymptote:
a line that a curve approaches but never crosses, as it heads towards infinity
Increasing:
y- values get bigger as you move from left to right
Decreasing:
y- values get smaller as you move from left to right
Steps for Graphing:
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
Exponential function form:
y=ab^k(x-d)+c
Mapping Notation:
(1/kx +d, ay+c)
The asymptote changes depending on the ? value
c
When c = -1, y = ?
-1
Remember to factor out the ? value
k
Rates of Increase/Decrease (‘b’ value)
For half-life
b=½
Rates of Increase/Decrease (‘b’ value)
For doubling, tripling,…
:b=2, b=3..
Rates of Increase/Decrease (‘b’ value)
For appreciation:
b = 1 + percent/100
Rates of Increase/Decrease (‘b’ value)
For depreciation:
b = 1 - percent/100
In y = ab^x
Y = result or future value
A = initial value (y intercept)
B = Rate of increase/decrease ratio
X = Number of times if has grown/decayed
In y = ab^x/xn
X = total time
Xn = Time it takes to grow/decay
