Problem 1 :
A cable company charges customers $60 per month for its service, with no installation fee. The cost to a customer is represented by
c(m) = 60m
where m is the number of months of service.
To attract new customers, the cable company reduces the monthly fee to $30 but adds an installation fee of $45. The cost to a new customer is represented by
r(m) = 30m + 45
where m is the number of months of service. Describe the transformations from the graph of c to the graph of r.
Problem 2 :
The total cost C (in dollars) to cater an event with p people is given by the function
C(p) = 18p + 50
The set-up fee increases by $25. The new total cost T is given by the function
T(p) = C(p) + 25
Describe the transformation from the graph of C to the graph of T.
Problem 3 :
You and a friend start biking from the same location. Your distance d (in miles) after t minutes is given by the function
d(t) = (1/5) t
Your friend starts biking 5 minutes after you. Your friend’s distance f is given by the function
f(t) = d(t − 5)
Describe the transformation from the graph of d to the graph of f
Problem 4 :
The function
t(x) = −4x + 72
represents the temperature from 5 P.M. to 11 P.M., where x is the number of hours after 5 P.M. The function
d(x) = 4x + 72
represents the temperature from 10 A.M. to 4 P.M., where x is the number of hours after 10 A.M. Describe the transformation from the graph of t to the graph of d.
Problem 5 :
A school sells T-shirts to promote school spirit. The school’s profit is given by the function
P(x) = 8x − 150
where x is the number of T-shirts sold. During the play-offs, the school increases the price of the T-shirts. The school’s profit during the play-offs is given by the function
Q(x) = 16x − 200
where x is the number of T-shirts sold. Describe the transformations from the graph of P to the graph of Q
Problem 6 :
The graph of
f(x) = x + 5
is a vertical translation 5 units up of the graph of f(x) = x.
How can you obtain the graph of
f(x) = x + 5
from the graph of f(x) = x using a horizontal translation?
Problem 7 :
When is the graph of y = f(x) + w the same as the graph of y = f(x + w) for linear functions? Explain your reasoning.
1) Vertical shrink with the factor of 1/2 and translating the curve up 45 units.
2) (p) is translating up 25 units vertically.
3) For every 5 minutes, your friend will be 1 mile away from you.
4) d(x) is reflection of the graph of t(x) with respect to y-axis.
5) Vertical stretch with the factor of 2 and translation vertically 50 units.
6) Horizontal translation of 5 units left.
7) Here -w tells us, we have to move the graph horizontally w units left.
Feb 25, 24 07:44 AM
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