Introduction to functions

Question 1

What is a function?

Answer 1

A rule to assign an input to an unique output value

Question 2

The input is called the:

Answer 2

independent quantity

Question 3

The output is called the:

Answer 3

dependent quantity

Question 4

In math, functions are usually represented by the letter:

Answer 4

f (sometimes g or h)

Question 5

Create a situation and provide a function.

Answer 5

f(x) = 0.18x

Where 18% is the gratuity and x is the cost of the meal.

Question 6

Is the equation x + y = 2 of function? Why/ why not?

Answer 6

It is!

Question 7

Is the equation x² + y² = 9 a function? Why/ why not?

Answer 7

It is not! A function only spits out ONE output for a given input.

Question 8

What is the vertical line test?

Answer 8

A test to help us see if a curve is a function by evaluating if a vertical line intersects the curve at MOST once.

Question 9

What is a One-to-one function?

Answer 9

If one output value is associated with EXACTLY one input value.

Question 10

Is this function one-to-one?

Answer 10

No, because because the output y has more than one input value x.
If f(2) = 2² = 4
If f(-2) = -2² = 4

Question 11

What is the horizontal line test?

Answer 11

A function is one-to-one if the horizontal line intersects the curve at most ONCE.

Question 12

Let f(x) = 2x² -2x
What is f(x) = 24

Answer 12

x = 4 or x = - 3

Question 13

Let f(x) = 2x² -2x.
Simplify

Answer 13

Answer: 2h - 18

Question 14

What is the domain of a function?

Answer 14

Set of all possible inputs denoted as Dsubf or dom(f)

Question 15

What is the range of a function?

Answer 15

Set of all possible outputs. Rsubf or ran(f)

Question 16

What is the domain of this function?

Answer 16

All real numbers

Question 17

What is the range of this function?

Answer 17

0 to infinity

Question 18

What would be the domain and range of this function?
dom(f) =
ran(f) =

Answer 18

Since you cannot do the square negative values:

Question 19

What would be the domain and range of this function?
dom(f) =
ran(f) =

Answer 19

Question 20

What is the domain and range of this function?
f(x) = ∛x

Answer 20

All values of x are defined since:

Question 21

If n is an even number ( n = 2, 4, 6, …) then the domain of f(x) = n√x is:

Answer 21

Question 22

If n is an odd number ( n = 1, 3, 5, …) then the domain of f(x) = n√x is:

Answer 22

R: all real numbers

Question 23

The domain of ANY polynomial (variables with positive integer exponents) is:

Answer 23

R: all real numbers

Question 24

What is the first idea to find the domain of a function?

Give an example in terms of A/B.

Answer 24

The fraction A/B is defined only if B ≠ 0

Question 25

What is the second idea to find the domain of a function? Give an example in terms of √A.

Answer 25

Question 26

Find the domain (set of all x) of this function.

Answer 26

Use the first idea to find the domain in this situation:

Question 27

Find the domain (set of all x) of this function.

Answer 27

Use the first idea to find the domain in this situation:

Question 28

What is a piecewise function?

Answer 28

It is a function where different formulas are use depending on the input.

Question 29

What would be the piecewise function of this example: A monthly phone plan costs $25 per month for up to 1000 minutes and charges $0.05 for each additional minute.

Answer 29

Question 30

What is the absolute value function?

Answer 30

Most popular piecewise function. States that if a value is greater or at 0 then the absolute value is the same. If the number is lower than zero you add a - to make it positive.

Question 31

What is considered a symmetric y-axis curve?

Answer 31

If its reflection in the y-axis is the same as the original graph.

Question 32

What is an even function?

Answer 32

A function is an even function if f(x) is equal to f(−x) for all the values of x. Its graph is symmetric with respect to the y-axis

Question 33

What is considered a symmetric x-axis curve?

Answer 33

If its reflection in the x-axis is the same as the original graph. (none of them are functions though)

Question 34

What is considered a symmetric origin curve?

Answer 34

If its reflection over BOTH axes is the same as the original graph. If replacing x with -x and y with -y gives you the same equation then the curve is symmetric about the origin.

Question 35

What is an odd function?

Answer 35

The odd functions are functions that return their negative inverse when x is replaced with –x. This means that f(x) is an odd function when f(-x) = -f(x).

Question 36

Answer 36

x not equal to -2

Question 37

Answer 37

x ≥ 0

Question 38

Is this f function even, odd, or neither?

Answer 38

odd

Question 39

Answer 39

Neither

Question 40

Answer 40

Neither

Question 41

Answer 41

He made a mistake in step 1.

Question 42

Answer 42

Even

Question 43

Answer 43

Neither

Question 44

Answer 44

odd

Question 45

Answer 45

Tamara's work is correct.

Question 46

Answer 46

f(2) DNE

Question 47

Answer 47

Question 48

Question 49

Answer 49

y-intercepts: 3, -3 x-intercept: -9 Symmetric on x-axis

Question 50

Answer 50

Symmetric on the origin

Question 51

What is the domain of this function? (interval notation)

Answer 51

(-infinity,-3)U(-3,3)U(3,infinity)

Question 52

What is the domain of this function? (interval notation)

Answer 52

(-9/16,infinity)

Question 53

Answer 53

A = -1 B = 6

Question 54

Answer 54

domain of f(x) = (-infinity,0]U[5,infinity) domain of g(x) = R

Question 55

f(-6) = f(-1) = f(7) =

Answer 55

f(-6) = 24 f(-1) = -1 f(7) = 12

Question 56

Answer 56

q(0.02) = 727/25

Question 57

Graph:

Answer 57

Answer: D

Question 58

Answer 58

Domaine: (-infinity, infinity) Range: (-infinity,6)