Chapter 5 Flashcards
How to do synthetic divison
check book
how to test function on graph
vertical line test
x-intercept
x coordinate where graph intersects x axis
y-intercept
y coordinate where graph intersects y axis
how many y intercepts in function
1
because for 1 input (0 as x value), 1 output
how to determine x intercepts for any function
set f(x)=0, then solve for x
How to solve for y intercepts
f(0)=y
when x=0
A function is increasing on the interval when
y1
function is decreasing on the interval when
y1>y2
but x1
function on the interval when
y1=y2
for every pair of numbers x1 and x2 in the interval
increasing function looks like
moves upwards from left to right as the independent variable assumes values from left to right on the interval
decreasing function looks like
moves downwards, from left to right, as the independent variable
constant function looks like
function value stays same as independent variable assumes values form left to right in interval
interval
part of a function
absolute mimimun
f(c) equal to or less than f(x)
absolute maximum
f(x) equal to or greater than f(x)
extreme values/extrema (plural of extremum)
minimum/maximum values of a function
relative minimum
open interval
relative maximum
open interval
relative extremum
relative minimum or maximum
extremum only applies to
x values
two kinds of asymptotes
horizontal and vertical asymptote
asymptote
line that graph gets closer in at least one direction along line
horizontal asymptote
line that graph gets closer to horizontally
vertical asymptote
line that graph gets closer to vertically
asymptotes are associated with_
rational functions
how to find vertical asymptote
when equation is in simplified form, set denominator to 0 and solve for x
how to find horizontal asymptote
value that y = f(x) approaches as x approaches positive or negative infinity (https://www.austincc.edu/pintutor/pin_mh/_source/Handouts/Asymptotes/Horizontal_an
d_Slant_Asymptotes_of_Rational_Functions.pdf)
Average rate of change
basically slope in functions, but it’s only for a certain interval
parts of division equation
dividend/divisor=quotient
parts of subtraction equation
minuend-subtrahend=difference
parts of addition equation
addend + addend= sum
parts of multiplication equation
multiplicand x multiplier (factors) = sum
horizontal asymptote when degree of numerator = degree of denominator
n/d
horizontal asymptote when degree of numerator>degree fo denominator
none, instead, it would be slanted
horizontal asymptote when degree of denominator> degree of numerator
x axis
In simplest form, the horizontal/vertical asymptote is the _
constant
If you divide rational functions, the quotient (without the remainder) is the _
asymptote
difference quotient
basically slope overall
difference quotient vs average rate of change
difference quotient: overall
average rate of change: interval
find difference quotient
book
find average rate of change
book
conjugate
reciprocal
