LO-U10T2 – #2: I can graph a cosine and secant function using transformations.
a)
Write the equation in standard form
f(x) = a cos[b(x - h)] + k where b 2 0 or f(x) = a sec[b(x - h)] + k where b > 0.
b) State the base equation and transformations.
c)
Create a table of points that moves the base graph through each of its transformations. You
must have 5 points in your table.
d) Sketch the graph using the points found in c). Be sure that the scale and spacing on the axes is
appropriate. Make your graph the size of at least 4 of a page.
e)
State the period, phase shift, and amplitude.
f) State the Domain and Range.
COSX
1. a)
-X +
cos(-x) =
c)
b) basery cost
2005[x - 5] + 3
horiz shift
pase V+E ky
'vert shrink 12
10,0
reflect across x-axis
(
10)
II, OJ
right It
(F/2, 1) 17/21/2/17 - 12/17 U
ITO (TO JT, 3/2]
(81, 1/2 / 131, 121 122 z
(21/312)
ادور 2ار

the height of the surface increases from the center out to the sides of the road.

step-by-step explanation:

as we move out we move away from the x-axis.

and as mentioned in the problem statement that height of a road increases when we move away from the center x.

hence proved that 3rd option

the height of the surface increases from the center out to the sides of the road.

is the correct option.

both triangles are similar because 2 is just smaller than the big one 1 is similar because they are facing different way's but are similar to each other

step-by-step explanation:

a) 40 more; b) old factory:   10%, new factory:   16%; c) week 4

explanation:

a) at week 0, we see in the graph that the new factory produces 190 specialty items.  

using the function, substituting 0 in for w,

this is a difference of 230-190 = 40.

b) the function for the old factory is written in the form f(x) = a(1+r)ˣ, where a is the original amount, x is the amount of time and r is the growth rate.   the equation for the old factory is ; 230 is in place of a and is the original amount; w is the amount of time; which means 1+r = 1.1.   this means that r must be 0.1 or 10%.

for the new factory, we find the percent of increase to find the growth rate; the formula for this is

between the first two points, the amount of change is 220-190 = 30; this gives us

30/190 = 0.158 ≈ 0.16 = 16%

c) at week 0, the old factory has 230 while the new factory has 190.

at week 1, the old factory has 230(1.1) = 253 while the new factory has 220.

at week 2, the old factory has 230(1.1²) = 278.3 while the new factory has 252.

at week 3, the old factory has 230(1.1³) = 306.13 while the new factory has 290.

at week 4, the old factory has 230(1.1⁴) = 336.743 while the new factory has 337.   this is the first week that the new factory surpasses the old.