CALCULUS 1000A FW21 - Homework Assignment #1
Due: September 19 at 11:59pm (EDT) on gradescope.ca
For full credit, ensure you show all your work and explain your reasoning. Simply stating the final answer
for any of the following questions will not result in full credit. Make sure you read and follow the submission
instructions for Gradescope.
1. (6 marks) For f (x) = ln(1
range of each result.
x2 ) and g(x) =
p
x + 2, find (f g)(x)and (g f )(x). Find the domain and
2. (5 marks) Sketch a graph of f (x) = 5(x + 4)3 3 by using a sequence of transformations of a well-known
function. For full points, make sure to describe the various transformations applied to the well-known
starting function. Only two sketches are required, one of the original well-known function and one of
f (x) itself.
3. As dry air moves upward, it expands and cools. If the ground temperature is 20 C and the temperature
at a height of 1km is 10 C
(a) (2 marks) Express the temperature T in C as a function of the height h (in kilometers), assuming
that a linear model is appropriate.
(b) (1 mark) What is the temperature at a height of 2.5 km?
(c) (1 mark) At what height is the air temperature -15 C ?
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