Graphical Reasoning (a & b)

[nycmathguy]

Section 2.2
105 (a & b)

Can you do 105 (a & b) as a guide for me to do a few others on my own? Ron Larson does not explain how this is done in the textbook.

Thanks

 

[MathLover1]

f(x)=x^4

a)
g(x)=f(x)+2
g(x)=x^4+2

function f(x) shifted 2 units up to get g(x)

b.
g(x)=f(x+2)
g(x)=(x+2)^4

function f(x) shifted 2 units left to get g(x)

 

[nycmathguy]

f(x)=x^4

a)
g(x)=f(x)+2
g(x)=x^4+2

function f(x) shifted 2 units up to get g(x)

b.
g(x)=f(x+2)
g(x)=(x+2)^4

function f(x) shifted 2 units left to get g(x)

Not too bad. I will do (c) and (d) when time allows. Big week for me. Moving to Brooklyn next Sunday. Oral surgery on Friday. I called out for this Thursday to rest up for my surgery. I also need to back up the rest of my stuff.

 

[nycmathguy]

f(x)=x^4

a)
g(x)=f(x)+2
g(x)=x^4+2

function f(x) shifted 2 units up to get g(x)

b.
g(x)=f(x+2)
g(x)=(x+2)^4

function f(x) shifted 2 units left to get g(x)

Determine if g is even, odd , or neither.

 

[MathLover1]

g(x)=(x+2)^4

g(x) = x^4 + 8 x^3 + 24 x^2 + 32 x + 16

To do this, you take the function and plug –x in for x, and then simplify

g(-x) = (-x)^4 + 8(-x)^3 + 24(-x)^2 + 32(-x) + 16=x^4 - 8 x^3 + 24 x^2 - 32 x + 16=>g(x) not equal to g(-x) =>the function is not even

also, g(-x) is not the exact opposite of what you started with (that is, if g (–x) = –g (x), so all of the signs are not switched), then the function is not odd

so, answer is: neither

 

[nycmathguy]

g(x)=(x+2)^4

g(x) = x^4 + 8 x^3 + 24 x^2 + 32 x + 16

To do this, you take the function and plug –x in for x, and then simplify

g(-x) = (-x)^4 + 8(-x)^3 + 24(-x)^2 + 32(-x) + 16=x^4 - 8 x^3 + 24 x^2 - 32 x + 16=>g(x) not equal to g(-x) =>the function is not even

also, g(-x) is not the exact opposite of what you started with (that is, if g (–x) = –g (x), so all of the signs are not switched), then the function is not odd

so, answer is: neither

This is the beauty of mathematics. It is a sequential subject.