MAC 1105 Pre-Class Assignment: Graphs of Common functions
Read sections 2.5 ‘Transformations of Functions’ to prepare for class
In this week’s pre-requisite module, we covered the topics evaluating square, cube, radical and absolute value
expressions and reading graphs. These are crucial skills needed for the conversation that we will be having this
week about graphs of functions and their transformations.
Below are some functions that are frequently encountered in Algebra. Look at page 283 in section 2.5 of the
textbook to see their graphs and their properties and answer the following questions.
1)
This type of function is called a constant function.
2) Graph the identity function 𝑔(𝑥) = 𝑥
a)
3) Check out the graph of the absolute value function in the text book and compare it with the identity
function.
a) How are they different?
b) How are they similar?
MAC 1105 Pre-Class Assignment: Graphs of Common functions
Read sections 2.5 ‘Transformations of Functions’ to prepare for class
c) Are their ranges different? Why is it so?
4) Use the Table 2.4 of Section 2.5 (Page 283) in the textbook to write down the characteristics of the
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standard quadratic function 𝑓(𝑥) = 𝑥 that are similar to the absolute value function 𝑔(𝑥) = |𝑥| .
However, the graphs of the two functions are different, why do you think that is?
5) What is another name for the graph of the standard quadratic function?
6) Why are the domain and range of square root function 𝑓(𝑥) = 𝑥 , restricted to [0, ∞)?
7) What is the equation for the standard cubic function? On which interval is it increasing?
8) Write whether the following statements are true or false:
a) The range of a cube root function is (− ∞, 0)
b) The graph of 𝑓(𝑥) = 𝑥 is symmetric with respect to y-axis
c) The domain of a standard cubic function is (− ∞, ∞)
After learning the graphs of common functions, you should be able to recognize the graphs of a constant
function, identity function, absolute value function, standard quadratic function, square root function,
standard cubic function and the cube root function. You should also know their characteristics (domain,
range, whether increasing or decreasing in each interval and symmetry) and how to graph these functions.
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9) Does knowing the graph of 𝑓(𝑥) = 𝑥 makes it easier to graph ℎ(𝑥) = 𝑥 + 3 ?