Question

Compare and contrast the following functions with repeat to symmetry, domain, and range
In each case explain the reason for the differences.
a) p(x) = x^pi

Answer 1

b) P(x) = x^22/7
c) P(x) = x^25/8
d) P(x) = x^223/71

Answer 2

@ganeshie8 @iambatman @greenglasses

Answer 3

So, to find the symmetry, you set the equation to P(-x). if P(-x) = P(x) it has symmetry (around the y-axis)

Answer 4

okay so i graphed them

Answer 5

Alright, then you've already pretty much solved your question then.

Answer 6

so thats for a)

Answer 7

so thats for b

Answer 8

so thats for c

Answer 9

Basically, if the x is put to the power of an irrational numbers, it does not exist for negative numbers.

Answer 10

and this is d

Answer 11

so what are the symmetry, domain and range for each one?

Answer 12

(when it's less than 1)

Answer 13

So symmetry is whether it has symmetry around the x-axis or y-axis.

Answer 14

You can see that of the four, only b does, right?

Answer 15

yep

Answer 16

well and b

Answer 17

Domain is the possible x-values. Two have xER (pretend that's that E-like symbol) but two only exist for values of x larger than 0.

Answer 18

Range is the possible y-values. You can see that for all but one, the only ones that exist are 0 or larger.

Answer 19

wait so now I'm confused. can you compare and contrast the domain and range and axis of symmetry for each one?

Answer 20

@ganeshie8

Answer 21

You know that only one has symmetry, right?

Answer 22

i think b has symmetry

Answer 23

Yes. So that means that in terms of symmetry, there's not much to compare other than to say that only b has symmetry along the y-axis.

Answer 24

Do you know how to dtermine domain and range?

Answer 25

nope

Answer 26

Okay, look at graph 1. the x^pi one.

Answer 27

What x-values have points on the graph?

Answer 28

well to pos inf

Answer 29

To positive infinity, from what value?

Answer 30

domain: x>0

Answer 31

Exactly. (including 0, but I assume you just used > because there's no equal to/greater than sign on the keyboard). So can you use that to figure out the domain for the other three graphs too?

Answer 32

but it excludes 0

Answer 33

No it doesn't. What's 0^(pi)?

Answer 34

okay so can you check all the domains and ranges i write

Answer 35

c) domain: all real numbers, range: all real numbers d) domain: all real numbers, range: all real numbers

Answer 36

for a) domain: all real numbers except x>_0, range: all real numbers except y>_0 b) domain: all real numbers, range: all real numbers except y>_ 0

Answer 37

for a) domain: x>_0, range: y>_0 b) domain: all real numbers, range: y>_ 0 c) domain: all real numbers, range: all real numbers d) domain: all real numbers, range: all real numbers

Answer 38

a) d) and b) look good, but c)'s range is off.

Answer 39

wait so can you retype everything cause I'm confused

Answer 40

a) domain: x is greater than or equal to 0 range: y is greater than or equal to 0
b) domain: x is all real numbers range: y is greater than or equal to 0
c) domain: x is...? range: y is...?
d) domain: x is all real numbers range: y is all real numbers

Answer 41

c) is x^(25/8), right? Look at the graph.

Answer 42

yea

Answer 43

so what's the domain and range?

Answer 44

d: x>_0 and range: all real #

Answer 45

So, negative y-values have points on the graph?

Answer 46

so can you explain to me in each case(symmetry, domain, and range) what causes the differences specifically?

Answer 47

i think my d and r are correct

Answer 48

For c) the range is y is equal to or greater than 0.

Answer 49

oh yea i understand

Answer 50

so can you explain to me in each case(symmetry, domain, and range) what causes the differences specifically?

Answer 51

Okay, let's put aside a) for now. Look at the other three. Why don't you put them in square root form?

Answer 52

Sorry, by square root form I mean root form.

Answer 53

I've got to go to sleep so I'll just tl;dr this alright? If you put c) in root form, you'll see than if x is negative, it'll be in an even root and to the power of an odd number, and the even root of a negative number to the power of an odd number is not real. however, if you put b) in root form, you'll see that it's both in an odd root and to the power of an even number, meaning that negative values of x are real. For d), same thing, just that since its greater than three, the equation resembles a cubic equation.