function graph

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The graph of f(x) :
a) Passes through or close to the point (0,-1).
b) Reaches a maximum of 2 at about x=0.7.
c) Reaches a minimum of about 0.4 at about x=1.8.
d) Reaches another maximum of 2 just before x=3
All numbers are approximate since we are estimating them from a graph.
13. y=f(x-1)
Everything that is happening at f(0) is now happening where x=1.
So on and so forth with other numbers.
The original f(x) is -1 where x=0.
The function f(x-1) will be -1 at x=1.
The entire graph is shifted one unit along the x-axis to the right.
f(x) reaches a maximum of 2 at about x=0.7.
For f(x-1), this maximum will occur when x=1.7.

14. y=1+f(x+2)
The function is shifted up one unit along the y-axis and
two units to the left along the x-axis.
a) Passes close to the point (2,0)
b) Maximum of 3 at x=-1.3
c) Minimum of 1.4 at x=-0.2
d) Maximum of 3 just before x=1
15. y=1+2f(x)
This time the function is at the same place along the x-axis
as f(x), but it is amplified by a factor of 2 and shifted up
the y-axis by one unit.
a) Passes close to the point (0,-1)
Because if f(0)=-1, then 1+2f(0)=1+2(-1)=1-2=-1
So this point ends up in about the same place,
but not exactly the same place because we really do not know
that the original f(x) is equal to -1 at x=0.
If f(0)=-a then 1+2f(0)=1+2(-a)=1-2a
b) Reach...