unit 2 quiz!!!! Flashcards
linear function
y= mx +b, domain & range both (-infinity, infinity)
quadratic function
ax2 + bx + c, domain (-infinity, infinity) and range dependent on which way parabola faces [min, infinity) or (-infinity, max]
absolute value function
y = abs. x, domain (-infinity, infinity) and range [min, infinity) or (-infinity, max]
constant function
y #= k, domain (-infinity, infinity), range = k
square root function
y= square root of x, domain and range BOTH [0, infinity)
cubic function
y= x cubed, domain and range BOTH (-infinity, infinity)
reciprocal function
y = 1/x, domain = x is NOT equal to zero {x|x =/= 0}, range y is NOT equal to zero (-infinity, 0) V (0. infinity)
exponential function
y= a to the xth power, domain= (-infinity, infinity), range = (0, infinity)
f(x) + a
shift up a
f (x +a)
shift left a
f(x) -a
shift down a
f(x-a)
shift right a
y= -f(x)
reflection over x axis
y= f(-x)
reflection over y axis
y= -f(-x)
reflection over the origin
y = -f(-x) reflection over the origin is the same as
rotation of 180 degrees
ORDER OF TRANSFORMATIONS!! IMPORTANT
1) LEFT/RIGHT
2) REFLECTIONS, STRETCH/SHRINK
3) UP/DOWN
stretching of the graph AWAY from the x axis
vertical stretch
squeezing the graph towards the x axis
vertical compression
a > 1
vertical stretch and horizontal compression notation
0 < a < 1
vertical compression and horizontal stretch notation
stretching of the graph away from the y-axis
horizontal stretch
squeezing of the graph towards the y- axis
horizontal compression
- For horizontal stretches/compression, multiply x–values in table by their reciprocal
measurement of how fast a function changes on average over a certain domain interval
average rate of change
change in output/change in input (like slope formula)
formula for average rate of change
*the domain and range of linear functions are all real numbers or (-infinity, infinity) except for vertical/horizontal lines
vertical stretch (graph away from x axis) /compression )graph towards x axis) f (5x) or f (1/5x) are characterized by the change i a y value- if it’s higher it’s a stretch, it it’s lower it’s a compression
horizontal stretch (graph away from y axis_ and compression (graph towards the y axis) are characterized by the change in an x value- if it’s higher it’s a stretch, if it’s lower it’s a compression
*always simplify where you can in the equation ex. (-x)2 is x2 and it must be written as such
when asked to list the transformations/graphing transformations do them in order
if you have to reflect over the origin, negate both values because it’s the same as a reflection over 180 degrees
