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Six problems from math 153 exam iib, covering topics such as domain of a function, average rate of change, graph analysis, and inverse functions. Each problem includes a detailed solution to help students understand the concepts and methods used to solve them.
Typology: Exams
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by
f (x) =
x + 1 x − 2
Part a (5 pts): What is the domain of f. Write your answer in interval notation.
Part b (5 pts): What is the average rate of change of f over the interval [3, 8].
calculator and determine the coordinates where f acheives a maximum. Your answer should be rounded to three (3) digits after the decimal place.
f (x) = x^3 − 4 x^2 − 2 x − 1
the following values.
f (x) =
3 x + 3 2 − 4 x
Part a (5 pts): Compute (f ◦ f )(2)
Part b (10 pts): Compute f −^1 (z)
the graph of y = 8f (4 − 3 x) + 1.
1 3 4 5 8
0
1
2
3
4
Teacher: A. Montgomery Name: Term: Spring 2008
Problem Possible Score 1 10 2 10 3 10 4 15 5 15 6 15 Total 75
m =
y 2 − y 1 x 2 − x 1 y − y 1 = m(x − x 1 ) (x − h)^2 + (y − k)^2 = r^2 d =
(x 2 − x 1 )^2 + (y 2 − y 1 )^2
ax^2 + bx + c = 0 =⇒ x =
−b ±
b^2 − 4 ac 2 a
