exam 3

Question 1

Section 11.1

Define a function.

Answer 1

For every input there is exactly one output.

Question 2

Section 11.1

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

Answer 2

domain

Question 3

Section 11.1

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

Answer 3

range

Question 4

Section 11.1

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

Answer 4

a function

Question 5

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.

Answer 5

intersects

Question 6

Section 11.1

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

Answer 6

Replace “x” with “-3.”

Question 7

Section 11.2

What is the slope formula of a linear function?

Answer 7

f(x) = mx + b

Question 8

Section 11.2

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

Answer 8

the point (0, 0)

Question 9

Section 11.2

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

Answer 9

m = y2 - y1 / x2 - x1

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

Question 10

Section 11.2

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

Answer 10

There is no slope. It exists as “0x”.

Question 11

11.3

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

Answer 11

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

Question 12

Section 11.3

What is the vertex in coordinates form?

Answer 12

(h, k)

Question 13

Section 11.3

Recall the parent graph of a parabola.

Answer 13

f(x) = x(SQ)

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

Question 14

Section 11.3

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

Answer 14

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

Question 15

Section 11.3

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

Answer 15

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

Question 16

Section 11.3

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

Answer 16

No reflection. Left 13. Shift down 7.

There is no reflection because the function is positive.

Question 17

11.3

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

Answer 17

Reflection. Shift right 4. Shift up 30.

Remember the horizontal shift is opposite of its value.

Question 18

11.3

The smallest possible output of a function is called the…

Answer 18

minimum value.

Question 19

11.3

The greatest possible output of a function is called the…

Answer 19

maximum value.

Question 20

11.3

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

Answer 20

B. output (y)

Question 21

11.3

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

Answer 21

Vertex.

Question 22

11.3

What is the formula for slope of a secant?

Answer 22

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

Question 23

11.3

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

Answer 23

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.

Question 24

11.4

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

Answer 24

from the bottom to the top.

Question 25

# 11.4 When defining the domain, think of it like reading a book...

Answer 25

from left to right.

Question 26

# 11.4 What is the parent graph of an absolute value function?

Answer 26

f(x) = | x | | left one, up one, left two, up two...

Question 27

# 11.4 What is the vertex formula for an absolute value function?

Answer 27

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

Question 28

# 11.4 If "a" is negative, then... | IF "a" in " a|x - h| + k"...

Answer 28

it faces downwards.

Question 29

# 11.4 If "a" is positive... | IF "a" in " a|x - h| + k"...

Answer 29

it faces upwards.

Question 30

# 11.4 What is the parent graph of a square root function?

Answer 30

f(x) = (SQRT of)x | right one, up one, right four, up two, right nine, up three...

Question 31

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

Answer 31

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

Question 32

# 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.

Answer 32

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.

Question 33

# 11.4 What is the parent graph of a cubic function?

Answer 33

f(x) = x(CUBED)

Question 34

# 11.4 A cubic function doesn't have a vertex, it has a...

Answer 34

point of inflection.

Question 35

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

Answer 35

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

Question 36

# 11.5 Define the sum function.

Answer 36

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

Question 37

# 11.5 Define the difference function. | Opposite of addition.

Answer 37

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

Question 38

# 11.5 Define the production function.

Answer 38

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

Question 39

# 11.5 Define the quotient function.

Answer 39

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

Question 40

# 11.5 Define the composite function.

Answer 40

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.

Question 41

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

Answer 41

domain. range.

Question 42

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

Answer 42

one element

Question 43

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

Answer 43

output. "x"

Question 44

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

Answer 44

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

Question 45

# 11.6 What is the horizontal line test?

Answer 45

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

Question 46

# 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).

Answer 46

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

Question 47

# 11.6 Two one-to-one functions f(x) and g(x) are inverse functions if ...

Answer 47

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

Question 48

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

Answer 48

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).

Question 49

# 11.6 A function and its inverse are always... | (when graphed)

Answer 49

symmetrical