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math 044 college algebra > exam 3 > Flashcards

exam 3 Flashcards

1
Q

Section 11.1

Define a function.

A

For every input there is exactly one output.

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2
Q

Section 11.1

The set of input values is called the (____) of the function.

A

domain

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3
Q

Section 11.1

The set of output values is called the (____) of the function.

A

range

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4
Q

Section 11.1

If no input (x) has more than one output (y), then it is…

A

a function

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5
Q

Section 11.1

If a vertical line can be drawn that (____) a graph at more than one point, the graph does not represent a function.

A

intersects

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6
Q

Section 11.1

What is the first step to solving this?
f(x) = 3x + 4, f(-3)

A

Replace “x” with “-3.”

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7
Q

Section 11.2

What is the slope formula of a linear function?

A

f(x) = mx + b

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8
Q

Section 11.2

When there is no identified y-intercept, it is…

A

the point (0, 0)

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9
Q

Section 11.2

What is the formula to find the slope of a function?

A

m = y2 - y1 / x2 - x1

When there are two points given of a graph, plug them in.

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10
Q

Section 11.2

What is the slope of this linear function?
f(x) = 2

A

There is no slope. It exists as “0x”.

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11
Q

11.3

What is the standard formula of a U-Shaped parabola?

A

f(x) = a(x - h)SQ + k

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12
Q

Section 11.3

What is the vertex in coordinates form?

A

(h, k)

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13
Q

Section 11.3

Recall the parent graph of a parabola.

A

f(x) = x(SQ)

Right one, up one, right two, up four…

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14
Q

Section 11.3

Explain the translation value of “h” in “(x - h) + k”

A

The translation of “h” is always the opposite of its assigned value.

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15
Q

Section 11.3

When graphing translations of “f(x) = (x - h)(SQ) + k”, how do you determine the shifts?

A

k = vertical shift/translation
h = horizontal shift/translation

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16
Q

Section 11.3

What is the rotation, horizontal shift, and vertical shift of the given function?
f(x) = (x + 13)(SQ) - 7

A

No reflection. Left 13. Shift down 7.

There is no reflection because the function is positive.

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17
Q

11.3

What is the rotation, horizontal shift, and vertical shift of the given function?
f(x) = - (x - 4)(SQ) + 30

A

Reflection. Shift right 4. Shift up 30.

Remember the horizontal shift is opposite of its value.

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18
Q

11.3

The smallest possible output of a function is called the…

A

minimum value.

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19
Q

11.3

The greatest possible output of a function is called the…

A

maximum value.

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20
Q

11.3

The maximum/minimum value is only the…
A. input (x)
B. output (y)
C. both (x, y)

A

B. output (y)

21
Q

11.3

You can find the minimum/maximum output by finding the…

A

Vertex.

22
Q

11.3

What is the formula for slope of a secant?

A

f(x+h) - f(x) / h

23
Q

11.3

How do you solve
f(x) = x(SQ) + 3x + 317
when you simplify the difference quotient
f(x+h) - f(x) / h?

A

Plug in (x+h) into the “x” placements of the f(x) equation given and then subtract the original f(x) equation from that, then divide it over h.

24
Q

11.4

When you define the range, think of it like an elevator moving …

A

from the bottom to the top.

25
Q

11.4

When defining the domain, think of it like reading a book…

A

from left to right.

26
Q

11.4

What is the parent graph of an absolute value function?

A

f(x) = | x |

left one, up one, left two, up two…

27
Q

11.4

What is the vertex formula for an absolute value function?

A

f(x) = a|x - h| + k

28
Q

11.4

If “a” is negative, then…

IF “a” in “ a|x - h| + k”…

A

it faces downwards.

29
Q

11.4

If “a” is positive…

IF “a” in “ a|x - h| + k”…

A

it faces upwards.

30
Q

11.4

What is the parent graph of a square root function?

A

f(x) = (SQRT of)x

right one, up one, right four, up two, right nine, up three…

31
Q

11.4

What is the standard (vertex) form of a square root function?

A

f(x) = (SQRT of)(x - h) + k

32
Q

11.4

Explain the difference to our square root function graph when a negative is outside the square root and when a negative is inside the square root.

A

When a negative is outside the square root, it reflects downwards. It flips vertically.
When a negative is on the inside of the square root, it reflects horizontally.

33
Q

11.4

What is the parent graph of a cubic function?

A

f(x) = x(CUBED)

34
Q

11.4

A cubic function doesn’t have a vertex, it has a…

A

point of inflection.

35
Q

11.4

What is the standard (vertex) form of a cubic equation?

A

f(x) = (x - h)(CUBED) + k

36
Q

11.5

Define the sum function.

A

For any two functions f(x) and g(x),
(f + g)(x) = f(x) + g(x).

37
Q

11.5

Define the difference function.

Opposite of addition.

A

For any two functions f(x) and g(x),
(f - g)(x) = f(x) - g(x).

38
Q

11.5

Define the production function.

A

For any two functions f(x) and g(x),
(f x g)(x) = f(x) x g(x).

39
Q

11.5

Define the quotient function.

A

For any two functions f(x) and g(x),
(f / g)(x) = f(x) / g(x).
g(x) cannot equal 0.

40
Q

11.5

Define the composite function.

A

For any two functions f(x) and g(x),
(f o g)(x) = f(g(x)).
Works vise verse for g(f(x)).
The symbol “o” is used to denote the composition of two functions.

41
Q

11.6

A function sends one value in the () to only one value in the ().

A

domain.
range.

42
Q

11.6

A one-to-one function that has every element in range corresponding to at most () in the domain.

A

one element

43
Q

11.6

In other words for each f(x) or () there is only one input () that will yield f(x).

A

output.
“x”

44
Q

11.6

Is this a one-to-one function?
{(-7,-5)(-5,-2)(-2,4)(3,3)(6,-7)}

A

This is a function.
It is a one-to-one function.

45
Q

11.6

What is the horizontal line test?

A

If a horiztonal line can intersect a graph at more than one point, the function is not one-to-one.

46
Q

11.6

Inverse functions (a) what a functions does. For example the point (3,7). The (b) gets sent to a (c). The inverse of f(x) will send a (d) to a (e).

A

a. undoes
b. 3
c. 7
d. 7
e. 3

47
Q

11.6

Two one-to-one functions f(x) and g(x) are inverse functions if …

A

(f o g)(x) = x
and
(g o f)(x) = x

48
Q

11.6

What are the five steps to finding the inverse of a function?

A
  1. Determine whether f(x) is one-to-one.
  2. Replace f(x) with y.
  3. Interchange x and y.
  4. Solve the resulting equation for y.
  5. Replace y with F-1(x).
49
Q

11.6

A function and its inverse are always…

(when graphed)

A

symmetrical

math 044 college algebra (4 decks)

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