LEVEL 5 MATH FUCTIONS REVIEW

1) The organizer of an air show asks two jet pilots to fly towards each other
while tracing the curve of f(x) = , where x and y are in meters.

What distance will separate the planes at their closest point?
(Hint: you're looking for the distance between the points of intersection of f(x)
and the line with a slope of 1 through the center of f(x). Draw a diagram!).

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2) The zeros of an absolute value function f(x) are -2 and 6.
The y-value of the vertex is 4.
a) What is the function rule?
b) Graph the function and list all the properties.
c) Solve f(x) m 2.

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3) An architect draws the model of a house's rafters on a Cartesian plane.
The axes are scaled in metres. Points C and D divide OB into three equal segments.

a) Find the rule for the abs. value function vertex A, sides AO and AB.
b) List all the properties for this particular situation.
c) If EF = 2 m. what is the vertical height between CD and EF?

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4) Once a plane takes off, the relation between its altitude in metres and
the time since take off (in seconds) is described by the rule h(t) = .
a) How long does the plane take to reach an altitude of 10,225 metres?
b) Find the rule for this function's inverse.
c) How long is the plane's altitude less than 1000 m.?

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5) List the vertical asymptote, horizontal asymptote, y-intercept and zero for:
(remember asymptotes are lines -- they have equations!!)
a) b) c) d)

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6) Myriam is 32 years old and wishes to buy some life insurance for 3 years.
She contacts four insurance companies, all of whom base their premiums
on the age of the client. The table shows fomulas for calculating the
four annual premiums she got from the insurance companies.
Which company offers the lowest price for 3 years of insurance?

company rule
A p1 = 17.70
B p2 =
C p3 = 9.10[ ] + 4.50
D p4 = 3.5 | x - 5 | + 4.10

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7) A construction company charges $75 per hour plus a $100 fixed fee for excavation work.
a) State the rule for calculating the average hourly rate for a job that lasts x hours.
b) For how many hours must they work to keep the average hourly rate below $85?
c) The company does some work for Samantha during which the average
hourly rate is $80.How long did they work?
d) Can the average hourly rate be $75? Explain.

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8) Given the four function rules

f(x) = x + 1 g(x) = x 2 - 2x -3 h(x) = k(x) =

find: a) g [f(x)] b) h [f(x)] c) k [f(x)]

        d) What kind of function is g [f(x)] ?

 

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9) A bicycle company estimates that the number of teens willing to buy its
new helmet follows the rule

a) How many customers would be willing to buy a helmet that costs $34?
b) By how many dollars must the company reduce the price (from $34) to sell 1000 more helmets?

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10) A trucking company estimates that its heavy equipment depreciates by 30% each year.
After 5 years, one of their trucks was worth no more than $12, 605.
a) What was the original price of the truck?
b) After how many years was the truck worth 10% of its original price?

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11) The data on the cost of a basket of groceries for a family with 2 children shows that
a basket which costs $110 today would increase by 1% per month for the next 3 years.
How many months must pass for this basket of groceries to cost $140?

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12) Determine the domain, range and zeros (if any) for:

a) f(x) = ln (x + 3) + 10 b) g(x) = log (10x + 20) - 1 c)

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