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unit 5 lesson 5 notes.notebook
1
April 08, 2015
Apr 87:04 AM
Warm Up
1. Given a. graph f(x)
f(6) = 3
f(1) = (1)2 + 1 = 2
f(5) f(6) = 3 (9) = 12
f (x) = 4 | x 5 | 7 absolute value, v
f(x) = 4[x 5] 7 step
Apr 87:13 AM
Prior to September, 2000, taxi fares from Washington DC to Maryland were as follows:
$2.00 for up to and including the first ½ mile, + $0.50 for each additional ½ mile increment.
Write the piecewise function for 0 to 2 miles. 2 , 0 < x < 1/2
2.50 , 1/2 < x < 1
3.00 , 1 < x < 1.5
3.50 , 1.5 < x < 2
Apr 87:36 AM Apr 87:38 AM
Apr 87:21 AM
Any equation that fits the form:
It is said that one variable “_________________________________” with or is“_____________________________” to another variable.
To solve a direct variation problem:
1. Plug given information into2. Solve for _____3. Rewrite equation using _____4. Plug new information into equation from step 3 and solve.
varies directlyproportional
y = kxk y = kx
what comes before varies is the "y"
what comes after varies is the "x"
Apr 87:22 AM
1. If y varies directly with x, and y = 24 when x = 16, find y when x = 12.
2. At your part time job, your pay is directly proportional to the number of hours you work. When you work for 13 hours you are paid $97.50. How much money would you make if you worked for 25 hours?
y = kx
24 = k (16)
k = 1.5
y = 1.5 x
y = 1.5 (12)
y = 18
y = kx
97.50 = k(13)
k = 7.50
y = 7.50x
y = 7.50(25)
y = $187.50
unit 5 lesson 5 notes.notebook
2
April 08, 2015
Apr 87:23 AM
3. The amount of money raised for the Junior-Senior Prom varies directly with the
number of tickets sold. The amount of money raised for 325 attendees is $11,375.
How many students need to attend the prom if the budget is $14,525.
415
Apr 87:24 AM
4. The number of goals scored by a soccer team is directly proportional to the number of shots on goal. If the Cary Imps Soccer Team scored 2 goals after 24 shots on goal, how many shots on goal should the team take to score two more goals?
24
Apr 87:15 AM
A relaonship that can be wrien in the form , where k is a nonzero
constant and , is an inverse variaon. Inverse variaon implies that onequanty will increase while the other quanty will decrease (the inverse, oropposite, of increase).
Domain: all real numbers except 0 ( x = 0)
Range: y = 0
vertical asymptote: x = 0
horizontal asymptote: y = 0
Apr 87:16 AM
Translaons of Inverse Variaons:
The graph of
Translates b units horizontally and c units vercally.
The vercal asymptote is x = b. The horizontal asymptote is y = c.
k tells how far the branches have been stretched from the asymptotes. = distance from the asymptote.
Apr 87:18 AM
Vertical asymptote: x = 3
Horizontal asymptote: y = 4
k = 1
right 3, up 4
Apr 87:18 AM
Vertical asymptote: x = 1
Horizontal asymptote: y = 0
left 1, reflect
k = 4
unit 5 lesson 5 notes.notebook
3
April 08, 2015
Apr 812:12 PM
VA: x = 1
HA: y = 2
right 1, up 2
domain: x = 1
range: y = 2
VA: x = 2
HA: y = 1
left 2, up 1
domain: x = 2
rangele: y = 1
Apr 812:12 PM
VA: x = 1
HA: y = 2
right 1, up 2
domain: x = 1
range: y = 2
VA: x = 2
HA: y = 1
left 2, up 1
domain: x = 2
rangele: y = 1
Apr 87:19 AM
Write the equaon described.
1. Write the equaon of that has asymptotes x = ‐ 4 and y = 5.
2. Write the equaon of that has asymptotes x = 5 and y = ‐ 3.
Apr 87:19 AM
Inverse VariaonInverse Variation:
"y varies inversely as x" y =“y is inversely proportional to x"
("k" is the constant of variation or constant of proportionality)
Find y when x = 18 if y varies inversely as x, and y = 3 when x = 4.
Y =
Using the inverse variation equation, y = , substitute the known value and solve
for the unknown. Y = , which will simplify to y =
Apr 87:20 AM
Find t when s = 20 if t varies inversely as s, and t = 5 when s = 16.
3. If b varies inversely as the cube of a and b = 3 when a = 2, find b when a = 5.
Apr 87:25 AM
