1.2 domain and range Flashcards
domain
x values. input. locaters on a graph
range
y values. output. max/mins
math moral laws
1- thou shalt not divide by zero
2- thou shalt not take the square root of a negative number.
3- the log of 0 does not exist
set notation
{ } curly brackets. when the domain and/or range are distinct numbers/ data and NOT an interval of values. Set number.
D:{2, 3,4,5}
R:{6,8,10}
closed intervals
brackets. describes intervals that do not include end points. point of a curve. Also called inclusive
interval notation
use parenthesis (). Continuous curves. Open dot.
what are the x values of a parabola?
zeros/roots/solutions/x-intercepts
how do you find the vertex for a parabola? y=ax^2+bx+c
-b/2a
what does the symbol E stand for?
is a member of. tells you what kind of value an interval describes
Inclusive
[ ] point on a curve. Solid dot.
True or false: is infinity inclusive?
No, because it cannot be bound. Infinity + 1!
Use ( )
Graph. x=4 domain and range.
Not a function. Vertical line.
D: {4}
R: (-inf, inf)
Graph y= -5. D and r.
Not a function. Horizontal line.
D: (-inf, inf)
R: {-5}
Graph y=3x +2. D and r.
Yes a function. Linear. Both domain and range are (-inf, inf)
Graph x^2 -5x+6. D and r.
Parabola. ax^2 + bx + c.
Yes function. Graph: find vertex. x= -b/2a. Plug x back into the function to find the y point. (x,y) is the vertex.
D: (-inf,inf)
R: [vertex, inf)
Note that it’s inclusive because the vertex is a point on the curve.
Graph 1/(x+2) domain
Graph has two curves. Parent function is y=1/x.
One in the first quadrant and one in the thirst quadrant. Asymptote at (0,0).
Math moral law says we can’t divide by zero. So to find domain,
SET DENOM = 0.
x+2=0.
x=-2.
D: (-inf,-2) U (-2,inf)
Graph y= √(3-4x) domain
Parent function: y=√x. Graph is a teacup.
Has a vertical rotation because of the -.
Math moral law says that we can’t take the square root of a negative number. Why? Because it’s imaginary.
Finding domain: SET GUTS ≥ 0.
3-4x≥0.
3≥4x
X≤3/4
D: (-∞, 3/4]
Graph log base 4 (x-5). And domain
Parent function: logs start at (1,0)
Graph will have an asymptote at (5,0) and a point on (6,0) with a continuous curve.
Math moral law says that log of 0 does not exist. Why? Because you can’t raise a number to a power that will equal 0. Logs and exponentials are inverses, so likewise, you cannot take the log of zero and get a number.
Finding domain: SET GUTS >0.
x-5>0
x>5.
D: (5,∞)
R: (-∞,∞)
Graph y=5sin2x and d and r
Sin waves are periodic. Starts at center line. Amplitude is 5. λ= 2π/b
