Introduction to functions Flashcards

1
Q

What is a function?

A

A rule to assign an input to an unique output value

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2
Q

The input is called the:

A

independent quantity

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3
Q

The output is called the:

A

dependent quantity

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4
Q

In math, functions are usually represented by the letter:

A

f (sometimes g or h)

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5
Q

Create a situation and provide a function.

A

f(x) = 0.18x

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

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6
Q

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

A

It is!

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7
Q

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

A

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

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8
Q

What is the vertical line test?

A

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

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9
Q

What is a One-to-one function?

A

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

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10
Q

Is this function one-to-one?

A

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

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11
Q

What is the horizontal line test?

A

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

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12
Q

Let f(x) = 2x² -2x
What is f(x) = 24

A

x = 4 or x = - 3

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13
Q

Let f(x) = 2x² -2x.
Simplify

A

Answer: 2h - 18

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14
Q

What is the domain of a function?

A

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

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15
Q

What is the range of a function?

A

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

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16
Q

What is the domain of this function?

A

All real numbers

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17
Q

What is the range of this function?

A

0 to infinity

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18
Q

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

A

Since you cannot do the square negative values:

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19
Q

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

A
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20
Q

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

A

All values of x are defined since:

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21
Q

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

A
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22
Q

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

A

R: all real numbers

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23
Q

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

A

R: all real numbers

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24
Q

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

Give an example in terms of A/B.

A

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

25
What is the second idea to find the domain of a function? Give an example in terms of √A.
26
Find the domain (set of all x) of this function.
Use the first idea to find the domain in this situation:
27
Find the domain (set of all x) of this function.
Use the first idea to find the domain in this situation:
28
What is a piecewise function?
It is a function where different formulas are use depending on the input.
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.
30
What is the absolute value function?
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.
31
What is considered a symmetric y-axis curve?
If its reflection in the y-axis is the same as the original graph.
32
What is an even function?
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
33
What is considered a symmetric x-axis curve?
If its reflection in the x-axis is the same as the original graph. (none of them are functions though)
34
What is considered a symmetric origin curve?
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.
35
What is an odd function?
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).
36
x not equal to -2
37
x ≥ 0
38
Is this f function even, odd, or neither?
odd
39
Neither
40
Neither
41
He made a mistake in step 1.
42
Even
43
Neither
44
odd
45
Tamara's work is correct.
46
f(2) DNE
47
48
49
y-intercepts: 3, -3 x-intercept: -9 Symmetric on x-axis
50
Symmetric on the origin
51
What is the domain of this function? (interval notation)
(-infinity,-3)U(-3,3)U(3,infinity)
52
What is the domain of this function? (interval notation)
(-9/16,infinity)
53
A = -1 B = 6
54
domain of f(x) = (-infinity,0]U[5,infinity) domain of g(x) = R
55
f(-6) = f(-1) = f(7) =
f(-6) = 24 f(-1) = -1 f(7) = 12
56
q(0.02) = 727/25
57
Graph:
Answer: D
58
Domaine: (-infinity, infinity) Range: (-infinity,6)