Calculus Exam 1

Question 1

How do you graphicall verify if an equation is a function

Answer 1

vertical line test

Question 2

Odd function notation

Answer 2

f(-x)=-f(x)

Question 3

Power function rule:

Answer 3

even powers have axis symmetry, odd powers have origin symmetry

Question 4

what is the domain for all polynomials

Answer 4

negative infinity, infinity

Question 5

how do you determine domain of rational function?

Answer 5

define bottom so that it can’t equal zero

Question 6

what is the ceiling function

Answer 6

smallest number greater than or equal to x

Question 7

name all parts in equation:
y=af(b(x+c))+d

Answer 7

a = vertical stretch/compression
f = function
b = horizontal stretch/compression
x = x value
c = horizontal shift
d = vertical shift

Question 8

what does the tangent line do?

Answer 8

line that best approximates the graph at a point

Question 9

what is the slope of y=e^x

Answer 9

1

Question 10

what is the inverse of y=e^x

Answer 10

y=lnx…. (f^-1)

Question 11

how can you check for a 1:1 function

Answer 11

use horizontal line test

Question 12

what types of functions have inverses

Answer 12

1:1 functions

Question 13

what is the domain of an inverse function?

Answer 13

the domain of an inverse is the range of the function

Question 14

what is the inverse of y=a^x

Answer 14

y=log(a)x

Question 15

what is the inverse of log(e)x

Answer 15

lnx

Question 16

unless restricted, trig functions are never..

Answer 16

1:1

Question 17

what is the domain of tan and sin

Answer 17

-pi/2, pi/2

Question 18

what is the domain of cos

Answer 18

0, pi

Question 19

what is the secant line

Answer 19

joining two parts of a curve

Question 20

instant rate of change is corresponds to..

Answer 20

slope of tangent line

Question 21

what does a limit describe

Answer 21

how a function behaves near a point

Question 22

3 steps to proving a limit:

Answer 22

1) start with how far f(x) can be from L (which is the epsilon)
2) manipulate to 0 < |x-3| < delta to form |x-3| < epsilon/3
3) can plug in any epsilon to equation to find delta

Question 23

what is the limit of sin(theta)/sin as x approaches 0?

Answer 23

1

Question 24

what must you do to prove limit of tan functions?

Answer 24

sandwich theorem

Question 25

3 points in continuity test

Answer 25

1) f(c) exists
2) limit of f(c) as x approaches c exists
3) limit of f(x) as x approaches c = f(c)

Question 26

where are constant functions continuous?

Answer 26

everywhere

Question 27

where are polynomials continous?

Answer 27

everywhere

Question 28

intermediate value property

Answer 28

whenever a function takes on 2 values, it also takes on all values in between

Question 29

1/x has a limit of.. as x approaches infinity

Answer 29

0

Question 30

how to calculate limit at infinity of rational function

Answer 30

must divide numerator and denominator by highest power of x in the denominator

Question 31

horizontal asymptotes are associated with …

Answer 31

limit of a function as x approaches infinity

Question 32

trig limits are different when x is approaching.. vs ..

Answer 32

approaching 0 vs infinity

Question 33

when must we prove a trig limit using sandwich theorem

Answer 33

limits involving infinity

Question 34

what is an oblique asymptote

Answer 34

slant line asymptote

Question 35

vertical asymptotes are associated with..

Answer 35

limit equalling neg/pos infinity

Question 36

what is indeterminate form

Answer 36

0/0