Mat 16A Midterm 1

Front 1

solving for intercepts

Back 1

for x, make y=0; for y, make x=0

Front 2

circle equation

Back 2

(x-h)^2+(y-k)^2=r^2

Front 3

getting radius from point on circle

Back 3

plug the point coordinates (x,y) into the circle equation with (h,k); solve for r

Front 4

slope-intercept form

Back 4

y=mx+b

Front 5

ratio vs. rate

Back 5

if x and y axis have same unit of measure, ratio; if x and y axis have different unit of measure, rate

Front 6

point-slope form

Back 6

y-y1=m(x-x1)

Front 7

standard (general) form

Back 7

ax+by+c=0

Front 8

perpendicular line slope

Back 8

negative reciprocal of initial slope (-1/m)

Front 9

Vertical line test

Back 9

if a vertical line intersects the graph more than once, it's not a function

Front 10

domain

Back 10

set of all values for which the function is defined (independent variable x)

Front 11

standard notation (for domain)

Back 11

something like x>1 or 0

Front 12

Interval notation (for domain)

Back 12

e.g. [-2, 6) ([] for inclusive, () for exclusive)

Front 13

range

Back 13

set of all values taken on by the dependent variable (y value)

Front 14

piecewise-defined function

Back 14

the f(x){ function; different functions depending on x-value

Front 15

one-to-one function

Back 15

to each value of the dependent variable, there corresponds exactly one value of the independent variable

Front 16

horizontal line test

Back 16

used to check if a function is one-to-one; same as vertical line test but horizontal

Front 17

(f○g)(x)

Back 17

is f(g(x))

Front 18

composite of f with g

Back 18

different wording for (f○g)(x)

Front 19

finding inverse functions

Back 19

replace f(x) with y, then swap x and y and solve for x; e.g. f(x)=x+1 would turn into x=y+1 which would turn into y=x-1 which would then be f

Front 20

If f has an inverse, f must be ________

Back 20

one-to-one

Front 21

Dividing-out technique

Back 21

dividing the numerator by the denominator to get an equation where the limit exists

Front 22

rationalizing the numerator

Back 22

multiplying the function by the conjugate of the numerator (e.g. (√(x+1)+1)/x * (√(x+1)-1)/(√(x+1)-1) )

Front 23

one sided limits

Back 23

when the limit doesn't exist at a point and differs from the left side (-) and the right side (+)

Front 24

Continuous functions

Back 24

functions that are not broken at a point; have no holes, jumps, or gaps

Front 25

getting the continuity of a function with a hole

Back 25

even if the point is filled, given a gap at x, with the graph going from -∞ to ∞, (-∞, 0), (0,∞)

Front 26

polynomials and continuity

Back 26

polynomials are always continuous in the intervals they are defined

Front 27

step function

Back 27

looks like stairs; functions consist of lines that shift up a certain amount when x changes to another integer; not continuous

Front 28

vertical asymptote

Back 28

f(x) approaches infinity at a point x; usually occurs in a function such as f(x)=1/x when x=0 and division by 0 occurs

Front 29

removable discontinuities

Back 29

discontinuities you can divide out; no vertical asymptote at the location, only a hole

Front 30

horizontal asymptote

Back 30

when y does not reach a certain value; occurs when finding a limit at ±∞

Front 31

degree

Back 31

power of the highest term (e.g. x^2+2x+1 would have a degree of 2

Front 32

leading coefficient

Back 32

the coefficient of the highest term (e.g. 3x^3+2x+1 would have a leading coefficient of 3)

Front 33

finding horizontal asymptotes

Back 33

given a function f(x)=p(x)/q(x), if the degree of q(x) is higher than that of p(x), it is at 0; if the degree of p(x) is equal to that of q(x), it is at a/b, a being the leading coefficient of P and b being the leading coefficient of q; if the degree of p(x) is higher than that of q(x), no horizontal asymptote

Front 34

horizontal asymptote at 0

Back 34

degree of q(x) given f(x)=p(x)/q(x) is higher than that of p(x)

Front 35

horizontal asymptote at a/b

Back 35

degree of p(x) and q(x) are the same given f(x)=p(x)/q(x); a and b are leading coefficients of p(x) and q(x), respectively

Front 36

no horizontal asymptote

Back 36

degree of p(x) is greater than that of q(x) given f(x)=p(x)/q(x)

Front 37

horizontal asymptote of f(x)=3x/2x^2

Back 37

0

Front 38

horizontal asymptote of f(x)=4x^2/8x^2

Back 38

4/8=1/2

Front 39

horizontal asymptote of f(x)=3x^2/x

Back 39

N/A