19.a Function Notations

Question 1

What does f(x) mean?

Answer 1

f of x
function of x

Question 2

The numbers a function uses are called __________, the numbers it produces are called _______________

Answer 2

The numbers a function uses are called INPUTS, the numbers it produces are called OUTPUTS

Question 3

does it have to be f(x), or can it be g(x)?

Answer 3

any letter can represent a function, it does not matter

Question 4

Solve:

Answer 4

Question 5

What is this?

Answer 5

The DOMAIN of the function
(the set of allowable inputs)

Question 6

When the domain is not specified, the number k will be in the domain only if f(k) is a ________________

Answer 6

When the domain is not specified, the number k will be in the domain only if f(k) is a REAL NUMBER

Question 7

For the purpose of the gmat, what are the two cases in which the output of a function is NOT a REAL number?

Answer 7

1. the denominator of the fraction is ZERO
2. the radicand of an even-indexed root is NEGATIVE

Question 8

Solve:

Answer 8

Question 9

Solve:

Answer 9

Question 10

What is the set of all possible outputs of a function called?

Answer 10

The range of the function

Question 11

What is the range of this equation?

Answer 11

The set of all real numbers greater than or equal to b

why?
because you can not take negative even-indexed root, so that part of the equation must be equal to or greater than zero.

Question 12

Solve:

Answer 12

Question 13

What is the range of this equation?

(n is positive even integer)

Answer 13

The set of all real numbers greater than or equal to c

why?
because you square x to an even power, so even if x is negative it will still result in a positive part of the equation

Question 14

Solve for the range of this equation:

Answer 14

The set of all real numbers greater than or equal to -16

Question 15

What is the range of this equation?

(n is a positive odd integer)

Answer 15

The range of f is the set of all real numbers

Question 16

Solve for the range of this equation:

Answer 16

Question 17

What is the range of this equation?

(a is not zero, and b is any real number)

Answer 17

The range of f is the set of all real numbers

Question 18

How can you find the range of other functions?

Answer 18

Test using:
MAXIMUM possible output
MINIMUM possible output
VALUES that can NOT be outputs

Question 19

Explain how you would solve this:

Answer 19

Text x values to maximize, test x values to minimize

Test other values, eg. range can not include 0 as numerator must be 0 for this to be the case, and its 4, so impossible.

Question 20

What is this called?

Answer 20

A compound function

Question 21

How do you solve a compound function?

Answer 21

Work from the INSIDE –> OUT

Question 22

The value you input into a function is the ____________, the function value is the ________________

Answer 22

The value you input into a function is the X COORDINATE, the function value is the Y COORDINATE

Question 23

How do you draw a function on the coordinate plane?

Answer 23

Question 24

If a > 0, the minimum output of function f occurs when you input x = _____________

Answer 24

If a > 0, the minimum output of function f occurs when you input x = _____________

Question 25

If a < 0, the minimum output of function f occurs when you input x = _____________

Answer 25

Question 26

What does this x value result in, in quadratic equations?

Answer 26

Question 27

Solve:

Answer 27