Question

Draw the graph of the function f(x) = |x| + 1 for the domain –5 ≤ x ≤ 5.

Answer 1

please note that
\[f(X)=x+1,\]
if\[x \ge 0\]
and:
\[f(x)=-x+1\]
if :
\[x <0\]
so:

Answer 2

Is there anything else I would have to do, or is that the graph itself of the function? I'm pretty dumb with this stuff

Answer 3

that is all! It is the graph itself!

Answer 4

Thank you so much! Do you think you could help me out with one more function thing?

Answer 5

Yes! I can!

Answer 6

Awesome thank you!! You're a life saver :)

Answer 7

Consider the function: f(x) = 2/5x - 4
a.) Find the inverse of f(x) and name it g(x). Show and explain your work.
b.) Tell why or how you know that f(x) and g(x) are inverses of each other.
c.) Draw the graphs of f(x) and g(x) on the same coordinate plane. Explain what about your graph shows that the functions are inverses of each other.

Answer 8

if f(x)=2/5 x-4, then, we have:
\[5f(x)=2x-20\]
so:
\[2x=5f+20\]
and finally:
\[x=\frac{ 5 }{ 2 }f+10\]
usually it is used y in place of f(x9; so:
\[x=\frac{ 5 }{ 2 }y+10\]
and inverse function of f is g(y) such that:
\[x=g(y)=\frac{ 5 }{ 2 }y+10\]

Answer 9

For B, what makes them inverse?

Answer 10

I draw their graphs:

in other words their graphs are identical!

Answer 11

With the inverse, how would I rename is as g(x) instead of f(x) like part A says?

Answer 12

I think that if I call g(x)=5/2 x+10
then I will get this: