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Alg 2 Hnrs Midterm Review (3.4 solving a system of equations with 3…
Alg 2 Hnrs Midterm Review
2.6 Special Functions
step function "piecewise-linear"
contains one expression
graph consists of line segments
greatest integer function: f(x)=[[x]]
round the inside value down to the greatest integer (unless it's a real world problem, then you round up)
range will consist of integers
absolute value
another type of piecewise-linear
contains an expression with absolute value bars
parent function: f(x)=|x|
piecewise "piecewise-defined"
uses 2 or more equations
domain is all real numbers
2.7 parent functions and transformations
constant function
f(a)=a
a=any number
domain is all real numbers
range consists of a single real number
basically is just a straight line
identity function
f(x)=x
all coordinates are (a,a)
domain and range are all real numbers
absolute value function
f(x)=|x|
domain is all real numbers
range is numbers greater than or equal to zero
quadratic function
f(x)=x^2
domain is all real numbers
range is the set of numbers greater than or equal to zero
transformations
reflections
when the PF is multiplied by a -1 , the function is reflected across the x-axis
when only the x is multiplied by a -1, the function is reflected across the y-axis
dilations
when a PF is multiplied by a nonzero number, it stretches or compresses vertically
coefficients > 1 stretch the graph
coefficients that are 0<x<1 compress
translations
up or down: when a constant, k, is added (up) or subtracted (down) to the parent functions
left or right: when a constant, h, is added (left) to x or subtracted (right) to x
3.4 solving a system of equations with 3 variables
step one
number your equations
step two
choose two equations to use elimination on and choose a variable to eliminate out
step three
repeat number two but with a different combo of equations (still eliminating the same variable as before)
step four
use the two new equations you have and solve by elimination
step five
take the values of the variables you just solved for and plug them into one of the original three equations to find the third variable
step six
your solution set looks like this: (x, y, z)
if you get 0=0 for one that means it has an infinite number of solutions for
those lines
if you get 0=another number, it's no solution
for those lines
to see if the final answer is no solution, you have to check if you get 0=another number for another combo of equations