PreCalc Chapter 1 Test Part 2

Question 0

a constant function can be horizontal and vertical

true or false

Answer 0

false–ONLY HORIZONTAL

Question 1

f(1)=4 really is

Answer 1

an ordered pair (1,4)

Question 2

f(x)=x^2

Answer 2

parent quadratic function

Question 3

f(x)=square root x

Answer 3

parent radical function

Question 4

f(x)=1/x

Answer 4

parent rational function (reciprocal function)

Question 5

what is the difference between 1/x and x/1 in terms of functions

Answer 5

1/x is the parent rational function and x/1 is a linear function with slope 1/1

Question 6

f(x)= [[x]]

Answer 6

greatest integer function (or, step function)

Question 7

what is a piecewise function

Answer 7

a function with pieces (normally 2 or 3)

Question 8

the greatest integer function takes the next integer ______

so -3.1 would go to __ and 2.9 would go to ___

Answer 8

-4, 2

it is also called the round-down function by some

Question 9

f(x)=x

Answer 9

identity function

Question 10

the constant function (f(x)=c) and the identity function (f(x)=x) are two special types of _____ functions

Answer 10

linear

Question 11

a piecewise defined function will always have at least one x-intercept or at least one y-intercept
true or false

Answer 11

true- defined means that the domain is all real numbers so it will have a y intercept at least

Question 12

what is a defined function

Answer 12

one that has a domain of all real numbers

Question 13

when performing a piecewise function, always ______ your solutions and make sure that your functions work

Answer 13

test

Question 14

a linear equation will always have an x intercept and a y intercept
true or false

Answer 14

false-constant functions will not have an x intercept

Question 15

what are the three types of transformations

what are the four types of translations

Answer 15

translation, reflection, dilation

up, down, left, right

Question 16

describe the translation
f(x)+c
f(x)-c
f(x+c)
f(x-c)

Answer 16

c units up
c units down
c units left
c units right

Question 17

describe the graph

h(x)=(x+2)^3 +1

Answer 17

cubic function shifted two units to the left and shifted up one

Question 18

when is there a reflection in the y-axis for a function?

x-axis?

Answer 18

y-axis: h(x)=f(-x)

x-axis: h(x)=-f(x)

Question 19

describe the graph

j(x)=-(x+3)^2 +1

Answer 19

quadratic function reflected over the x-axis, shifted three units to the left and up one

Question 20

when the shapes are congruent or unchanged after a transformation, the transformation is a _________
what kinds of transformations are included

Answer 20

rigid transformation

translations, reflections

Question 21

transformations that cause shapes to change (horizontal or vertical stretches) are _____________
example?

Answer 21

nonrigid transformations

dilation

Question 22

when will a function vertically stretch?

Shrink?

Answer 22

n*f(x) when n<-1(-infinty,-1) or n>1(1, infinity)

n*f(x) when -1<n<1 (-1,1)

Question 23

g(x)=(x-1)^3 +2
what is the parent function?
use function notation to write g in terms of f

Answer 23

f(x)=x^3
g(x)=f(x-1) +2
***Remember not to include the ^3, as that is implied in f(x)

Question 24

horizontal shifts, vertical shifts, and reflections are called _____ transformations

Answer 24

rigid

Question 25

A reflection in the x-axis of y=f(x) is represented by h(x)= ________, while a reflection in the y-axis of y=f(x) is represented by h(x)=__________

Answer 25

-f(x) | f(-x)

Question 26

A nonrigid transformation of y=f(x) represented by g(x)=cf(x) is a _________ when c<-1 or c>1 and a ______ _______ when -1

Answer 26

vertical stretch, vertical shrink

Question 27

in (f of g)(x), what is the domain?

Answer 27

the domain of f of g is the set of all x in the domain of g such that g(x) is in the domain of f

Question 28

what is the composition of functions

Answer 28

taking one function and plugging it into another function (not commutative)

Question 29

is composition of functions commutative? what does this mean?

Answer 29

no- this means that you will get the same answer in reverse (think addition, multiplication [4+2=2+4])

Question 30

is (f of g)(x) muliplication

Answer 30

No

Question 31

``` how do you decompose a composite function? decompose h(x)=1/(x-2)^2 ```

Answer 31

first find the simplified function (this is your f(x)), then think, what do i plug in (g(x)), to get what I have now? f(x)=1/x^2 g(x)=x-2 ***Note that the ^2 is outside of the parentheses. This is why you cannot have f(x)=1/x and g(x)=x-2^2--> you could have g(x)=(x-2)^2

Question 32

what are transcendental functions

Answer 32

mix of two types of functions (1/x^2) quadratic and rational

Question 33

what are the 4 types of functions

Answer 33

polynomial, rational, radical, trigonometric (i dont think we need to know this just in case though)

Question 34

two functions f and g can be combined by the arithmetic operations of ________,_________,_________, and ____________to create new functions

Answer 34

addition, subtraction, multiplication, division

Question 35

The _____ of the function f with g is (f of g)(x)=f(g(x))

Answer 35

composition

Question 36

f(x)=x^2 +6 g(x) square root (1-x) | divide these

Answer 36

x^2 +6/square root of (1-x) ---cannot have square roots on the bottom (multiply top and bottom by square root (1-x))---- x^2 +6 square root (1-x)/1-x

Question 37

what is (f-g)(0)

Answer 37

f(0)-g(0)

Question 38

a set ordered pair (mapping, x/y chart, etc.)

Answer 38

relation

Question 39

Two techniques for fitting models to data are called direct and iverse _______ and least squares ________

Answer 39

variation, regression

Question 40

Statisticians use a measure called the ______ of _____ _______to find a model that approximates a set of data most accurately

Answer 40

sum, square differences

Question 41

The linear model with the least sum of square differences is called the ______ ______ _______ line

Answer 41

line of regression

Question 42

An r value of a set of data, also called a ________ _________, gives a measure of how well a model fits a set of data. what is the worst of these? best?

Answer 42

correlation coefficient | 0, 1

Question 43

direct variation models can be described as "y varies directly as x," or "y is _______ ________ to x"

Answer 43

directly proportional

Question 44

In direct variation models of the form y=kx, k is called the ____ of ____

Answer 44

constant, variation

Question 45

The direction variation model y=kx^n can be described as "y varies directly as the nth power of x," or "y is ____ _____ to the nth power of x"

Answer 45

directly proportional

Question 46

The mathematical model y=k/x is an example of _____ variation

Answer 46

inverse

Question 47

The joint variation model z=kxy can be described as “z varies jointly as x and y,” or “z is ________ ________ to x and y.”

Answer 47

directly proportional

Question 48

what is mathematic modeling

Answer 48

coming up with the equation

Question 49

what is a model?

Answer 49

an equation

Question 50

y varies directly as x y is directly proportional to x y=kx for some nonzero constant k

Answer 50

direct variation

Question 51

what is k in y=kx?

Answer 51

constant of variation, also the rate

Question 52

what is the equation for state income tax | what kind of variation does it have

Answer 52

state income tax=k(gross income) (T=k*g where T is the dependent variable and g is independent) direct

Question 53

what must you have in order to find k-the constant of variation

Answer 53

initial condition

Question 54

inverse variation says as one gets bigger, _________________________

Answer 54

the other gets smaller

Question 55

y=k/x is ______ variation. It is the opposite of _____

Answer 55

inverse, direct

Question 56

z=kxy

Answer 56

joint variation (z varies jointly as x and y)

Question 57

what is the equation for Interest

Answer 57

I=P*r*t | since k is also rate, you could say I=k(P)(t

Question 58

how do you find a lines equation and graph a scatter plot on your calculator?

Answer 58

lines equation given a lot of points- hit stat, edit, enter x values in L1 and y values in L2, make sure you have the same number of data entries, hit stat again, calc, LinReg, make sure Xlist says L1 and Ylist says L2, calculate this will give you your equation!!! to plot a scatter graph- go to y=, graph the line you got above^ (may have to adjust windows) then hit Stat Plot (second y=), plot 1 on, choose type, graph (should get a line with plots)

Question 59

what kind of variation will these ordered pairs have? | 5, -3.5)(10, -7)(15, -10.5)(20, -14)(25, -17.5

Answer 59

Direct---although technically the numbers are getting smaller, the positive values are increasing

Question 60

z varies directly with the square of x and inversely with y with a constant variation of 2/3 how would you write this?

Answer 60

z=2x^2/3y (separate your fraction)

Question 61

S=4pi r^2 | how would you use variation terminology to say this aloud

Answer 61

The surface area of a sphere varies directly as the square of the radius r (your constant of variation is 4pi [you will never say a number])

Question 62

how would you use variation terminology to say A=1/2bh

Answer 62

the area of a triangle is jointly proportional to its base and height

Question 63

Inverse operations _________ each other

Answer 63

undo

Question 64

what is f^-1(x)

Answer 64

inverse of f (-1 has new mathematical value!)

Question 65

what does a graph's inverse do | what kind of symmetry do they have

Answer 65

switches x and y | reflectional symmetry over the line y=x

Question 66

for a function to have an inverse, it must pass (Horizontal/Vertical) Line Test

Answer 66

BOTH- it must pass vertical to be a legitimate function. It must pass horizontal to have an inverse

Question 67

an inverse cannot fail (Horizontal/Vertical) line test

Answer 67

I think just Vertical???

Question 68

The domain of a function = the _____ of its inverse. | the range of a function = the _____ of its inverse

Answer 68

range, domain

Question 69

how do you prove f(x) and g(x) are inverses of eachother

Answer 69

``` use composite functions (analytically) plug g(x) into f(x) [f(g(x))] and you will get x ```

Question 70

a function is __________ if it passes Horizontal and Vertical line test

Answer 70

one to one

Question 71

only __________ have an inverse function

Answer 71

one to one

Question 72

how would you make f(x)=x^2 a function with an inverse

Answer 72

restrict the domain (x>_ 0)

Question 73

in a piecewise function, the ranges of the starting functions are the _________ of the inverse functions

Answer 73

domains

Question 74

If the composite functions f(g(x)) and g(f(x)) both equal x, then the function g is the ______ function of f

Answer 74

inverse

Question 75

The inverse function of f is denoted by

Answer 75

f^-1

Question 76

The domain of f is the ____ of f^-1 and the, and the ______ of f^-1 is the range of f

Answer 76

range, domain

Question 77

The graphs of f and f^-1 are reflections of each other in the line ___

Answer 77

y=x

Question 78

A function is _____ when each value of the dependent variable corresponds to exactly one value of the independent variable

Answer 78

one-to-one

Question 79

A graphical test for the existence of an inverse function of f is called the _____ Line Test

Answer 79

Horizontal

Question 80

To reflect over x axis, make _ values negative | Vice versa

Answer 80

y

Question 81

Be careful with distributing negatives in reflection cases | Square root of (x+6) reflected in both x and y axes is...

Answer 81

-square root of -x-6

Question 82

Remember when a graph is up 3 and a point is (1,7), it's technically

Answer 82

(1,4)

Question 83

If f(x)=x^2 and you plug in 4t, what do you get

Answer 83

(4t)^2=16t