Functions 1.1-1.3 Flashcards
How many outputs can a function give to be classified a function?
Only 1
The two domain rules?
Can’t have a 0 in fraction, and can’t have a negative in an even root
What is the quadratic formula?
(-b+-sqrt b^2-4ac)divided(2a)
What is the way to find a vertex between 2 zeros?
Find the midpoint value (x) and then plug the value into your function to find f(x)
Midpoint formula (when you have no zeroes?)
-(b)/2a
What does sqrt x look like as a function?
Like the top left corner of a square in the first quadrant
What does 1/x look like as a function
A 90° angle that looks like an L that has asymptotes for the Y and X axis
What does 1/x^2 look like as a function?
A 90degree angle with asymptotes for both axis that reflects over the y-axis. 
What does e^x look like?
A slope upwards with asymptote at the x axis and a y intercept at 1
What does lnx look like?
A slope like the top left corner of a square that starts in quadrant 4 and passes through 1 on the x axis with an asymptote for the y-axis.
Definition of even function
f(-x)= f(x)
Definition of an odd function
f(-x)=-f(x)
Definition of abs value function
Junk if junk is > or = 0
-(Junk) if junk is < 0
Make sure you know the trig functions look, domain and range.
Do you?
Definition of polynomial?
Did you write it down?
Does sqrt of (a + b) = (sqrtA)+ (sqrtB)?
No!!! This only works with multiplication or division under a radical.
Vertex form equation
y=a(x-h)^2 +k (h,k) is the vertex point.
When the leading degree is odd what is the end behavior?
Positively opposite diagonally.
When the leading degree is even what is the end behavior?
Reflect across y-axis think like U|U
g(x)=f(x)+-k means what?
g(x) is f(x) shifted up or down k units.
g(x)= f(x+-k) means what?
g(x) is f(x) shifted left or right k units.
g(x)=-f(x) means what?
g(x) is f(x) reflected across the x axis.
g(x)=f(-x) means what?
g(x) is f(x) reflected across the y axis.
g(x)=kf(x) means what?
It means that g(x) is f(x) vertically stretched or shrinked by a factor of k. If k is between 0 and 1, the graph shrinks. If it is greater than 1 it stretches.
g(x)=f(kx) means what?
It means that g(x) is f(x) stretched or shrinked horizontally by a factor of k. If k is between 0 and 1 it shrinks. If it is greater than 1 it is stretched.
Formula to find slope In standard form?
(-A/B)
Domains of functions that are combined are found how?
By finding where domains interlap. NOT the Endpoints of both domains.
