Chapter 1: Review of functions

Question 1

Suppose f is defined for all x near a with x > a. If f(x) is arbitrarly close to L for all x sufficiently close a with x>a, we write

lim_x→a⁺f(x) = L

Answer 1

Right- Sided Limit

Question 2

Assume f is defined for all x near a except possibly at a. Then lim_x→a f(x) = L if & only if lim_x→a⁺ = L &

lim_x→a^-f(x) = L

Answer 2

Relationship between One - Sided & Two Sided Limits (Theorem 2.1)

Question 3

An _______ function f has the property that f(-x) = f(x), for all x in the domain

Answer 3

Even Function (Also symmetric about the y-axis)

Question 4

A graph is symmetric with respect to the ______ axis if whenever the point (x,y) is on the graph, the point (x,-y) is also on the graph

Answer 4

Symmetric with respect to the x-axis

Question 5

A graph is symmetric with the respect to the ______ whenever the point (x,y) is on the graph, the point

(-x,-y) is also on the graph

Answer 5

Symmetric with respect to the origin

Question 6

A function is _________ on a domain D if each value of f(x) corresponds to exactly one value of x in D

The ____________ says that every horiziontal line intersects the graphs of a one to one function at most once

Answer 6

One to One, Horizontal line test

Question 7

What is the domain of both sec^-1 & Csc ^-1 ?

Answer 7

[x: /x/ _>_ 1]

Question 8

Suppose f is defined for all x near a with x < a. If f(x) is arbitrarly close to L for all x sufficiently close to a with x < a, we write

lim_x→a^- f(x) = L

Answer 8

Left - Sided Limit

Question 9

What is the restriction of csc^-1?

Answer 9

[-π/2, π/2] & undefined at 0

Question 10

An _______ function f has the property that f(-x)= -f(x), for all x in the domain

Answer 10

Odd function (Also symmetric about the origin)

Question 11

What is the domain of tan^-1 & cot^-1?

Answer 11

[-infinity, +infinity]

Question 12

A graph is symmetric with respect to to the ______ axis if whenever the point (x,y) is on the graph, the point (-x,y) is also on the graph

Answer 12

Symmetric with respect to the y-axis

Question 13

Let P(x,y) be a point on a circle of radius r assoicated with the angle delta, then sin= ?, cos=?, tan=?, cot=? sec=?, csc=?

Answer 13

(Trigonometric Functions definitions)

Sin= y/r

Cos= x/r

Tan=y/x

Cot= x/y

Sec= r/x

Csc= r/y

Question 14

A _________ f is a rule that assigns to each value x in a set D a unique value denoted f(x). The set D is the ________ of the function & the _______ is the set of all values of f(x) produced as x varies over the entire domain

Answer 14

Function, Domain, & the Range

Question 15

What is the restriction for inverse tan^-1 ?

Answer 15

[-π/2, π/2]

Question 16

Given two functions f & g, the ________ ________ is defined by f(g(x)), where its evaluated in two steps y=f(u), where u=g(x). The domain of f(g(x)) consist of all x in the domain of g such that u = g(x) is in the domain of f

Answer 16

Composite Function (Defintion)

Question 17

If f(x) is arbitrarily close to L (as close to L as we like) for all x sufficiently close (but not equal) to a , we write______

Answer 17

lim_x→af(x) = L (Preliminary denfinition of a function)

Question 18

What is the restriction on the inverse of cot^-1?

Answer 18

[0,π]

Question 19

For any base b > 0, with b doesnt = 1, the ___________, denoted y=log_b^x, is the inverse of the exponential function y=b^x

The inverse of the natural exponential function with base b = e is the ______________, denoted y=lnx

Answer 19

Logarithmic function base b, natural logarithm function

Question 20

What is the restricition of sec^-1?

Answer 20

[0,π] but its undefined at π/2

Question 21

Every vertical line intersects the graph at most once, if the graph fails this test it does not represent a function

Answer 21

Vertical LIne Test