Vocab/Things to Know
What are the 4 congruence postulates/theorems?
SSS, SAS, ASA, AAS
Given f(x)=-4x-10 and f(x)=10, find x.
x=-5
If you are raising a power to a higher power, what operation do you do?
Multiplication!
(xn)m=xnm
What is the basic formula for exponential functions? Describe what a and r mean within the formula.
f(x)=a*rx
where a=initial value and r=rate or ratio
In Dilations, segments lengths are not preserved, but these features are. (name at least 2)
What are angle measures, betweenness of points, and collinearity?
All angles in a triangle add up to what?
180 degrees!
What is the domain of the following function?
g(t)=sqrt(5t-6)-4
5t-6>0
Domain is all real values of x such that t is greater than or equal to 6/5
What do you do when you have a negative exponent?
Flip!
x-n=1/xn
Consider the function below:
g(x)=2*0.75x
is this an exponential growth or decay function?
Decay since r<0
Find the coordinates of B" when A(5, 0), B(5, 5), and C(2,4) undergo the following composition: translate (x, y)-->(x+6, y-5), then rotate counterclockwise 270 degrees.
What is B"(0, -11)?
What operation do you do to the exponents with the following expression?: (xn)(xm)
You add them:
xn+m
What is the difference between absolute maximum and relative maximum?
Absolute: the single highest point
Relative: all the highest points within the window we can see
Simplify the radical by removing all perfect squares from inside the radical:
sqrt(28)
Consider the function below:
f(x)=5*3x
what is the initial value?
a=5
If angle AOC is a right angle and angle AOB is 74 degrees, what is the measure of angle BOC?
90-74=16
In f(x)=mx+b, which is the input and which is the output?
f(x): output
x: input
What is the formula for average rate of change?
Simplify: (3x4)2
9x8
Graph the following exponential function:
f(x)=3*2x
Points at (0,3) and (1,6)
What does CPCTC stand for?
Corresponding parts of congruent triangles are congruent
Which transformation is non-rigid?
Dilation
Determine whether the following situations are modeled by linear functions or exponential functions.
I. The annual cost of your renter’s insurance policy $1000 per year. Each year it increases by $80.
II. The value of your car started at $30500, and reduces by 35% each year.
I: linear since it increases by a constant amount ($80) each year
II: exponential since it is reducing by a percentage, meaning the amount is changing but it's still reducing at a constant rate
Simplify: -(x2y5)4
-x8y20
If a graph has points at (0,1) and (1,2), what is the exponential function that represents it? (Hint: find a and r)
f(x)=1*2x
The legs of an isosceles triangle have lengths (x+1) and (-x+7). The base has length (3x-3). What is the length of the base?
x+1=-x+7
2x=6
x=3 so 3(3)-3=9-3=6