Functions

Question 1

What should we be checking for when evaluating the domain of a function?

Answer 1

The two major concerns for the domain of a function, for GMAT purposes, are that 1) we can’t take the square root of a negative number and 2) we aren’t allowed to divide by 0.

Question 2

How to find the (x,y) coordinates in a function

Answer 2

The input you plug into the function [i.e. ‘x’] is x. The result of the function is y.

Question 3

Determining range of function

Answer 3

for a function in the form of f(x) = kx^n + c where n is positive and k is nonzero:

• if k > 0 then the range of f(x) is all real numbers greater than or equal to c
• if k < 0 then the range of f(x) is all real numbers less than or equal to c

Question 4

determining domain of function by looking at graph

Answer 4

read graph from left to right. see where the arrows of the graph start and end

Question 5

determining range of function by looking at graph

Answer 5

read graph from top to bottom. see where parabola starts or ends [the curve] and where it starts is the y

Question 6

what is the vertical line test

Answer 6

the vertical line test states that there can only be one point on the graph that intersects line vertically. in other words, there can only be one value of y per each (x,y) pair

Question 7

what is the vertical line test

Answer 7

the vertical line test states that there can only be one point on the graph that intersects line vertically. in other words, there can only be one value of y per each (x,y) pair

Question 8

Critical rule of sequences

Answer 8

Every sequence has a rule or a formula that dictates how the sequence works. In order to make any conclusions about the terms in the sequence, this rule must be known.

Question 9

What is an arithmetic sequence

Answer 9

An arithmetic sequence is a sequence in which the difference between every pair of two consecutive terms is the same.

An arithmetic sequence has the formula

an=a1 + (n-1)d

where a*n is the nth term in the sequence, a1 is the first term, and d is the common difference

n=number of terms

Question 10

The sum of the first n terms of an arithmetic sequence is

Answer 10

sn = n/2(a1 + an)

n=number of terms
a1= first term in set
an=last term in set

Question 11

A geometric sequence (or geometric progression) is one in which the ratio between every pair of two consecutive terms is the same.

Answer 11

represented by formula

a*n = a1 * r^n-1

a*n=nth term
a1= first term
r = common ratio

Question 12

what is a domain?

Answer 12

the set of all numbers that a function can use [i.e. the inputs]

the number that goes in f()

Question 13

what is a range?

Answer 13

the set of all outputs that a function can generate

what f(x) is equal to