There are a handful of functions that you need to have on your fingertips,
in the following sense:
Here are the seven ‘basic models’ to be studied in this lesson.
Each is shown in the same window, from
[beautiful math coming... please be patient]
$\,5\,$ to $\,5\,$ on the xaxis,
and from $\,4\,$ to $\,4\,$ on the yaxis.
The scales on the xaxis and yaxis are identical.
That is, a distance of $\,1\,$ on the
xaxis is the same as a distance of $\,1\,$ on the yaxis.
the identity function [beautiful math coming... please be patient] $f(x)=x$ 
the squaring function [beautiful math coming... please be patient] $f(x)=x^2$ 
the cubing function [beautiful math coming... please be patient] $f(x)=x^3$ 
the square root function [beautiful math coming... please be patient] $f(x)=\sqrt{x}$ 
the absolute value function [beautiful math coming... please be patient] $f(x)=x$ 
the reciprocal function [beautiful math coming... please be patient] $f(x)=\frac1x$ 
a constant function [beautiful math coming... please be patient] $f(x)=3$ 
You may want to review
Domain and Range of a Function
from the Algebra I curriculum.
Key concepts are repeated here for your convenience.
The domain of a function is the set of all its allowable inputs.
The domain convention states that if the domain of a function is not
specified,
then it is assumed to be the set of all real numbers for which the function is defined.
The domain of a function $\,f\,$ is denoted by
[beautiful math coming... please be patient]
$\,\text{dom}(f)\,$.
The range of a function is the set of all its outputs, as the inputs vary through
the entire domain.
The range of a function $\,f\,$ is denoted by
[beautiful math coming... please be patient]
$\,\text{ran}(f)\,$.
Since the domain and range are sets,
correct set notation must be used when reporting them;
it may be helpful to review
interval and list notation.
Remember that the symbol $\,\mathbb{R}\,$ denotes the set of real numbers.
The domain of a function is usually easy to determine from a formula for the function.
Numbers that cause division by zero must be excluded from the domain.
Anything inside an even root (square root, fourth root, etc.) must be greater than or equal to zero.
However, the range of a function is usually more difficult to determine from a formula.
It is easy to get both the domain and range of a function from its graph, as discussed next.
Consider the graph shown at right: this is the absolute value function, with a restricted domain. As always, a typical point on the graph is an (input,output) pair; the $\,x$value of the point is the input, and the $\,y$value of the point is the output. As the point $\,P\,$ is moved through the entire graph, all the $\,x$values indicated in red are taken on. These are the allowable inputs for this function. Therefore, the domain of this function is the interval $\,[2,5)\,$. Notice that $\,2\,$ is in the domain of the function, indicated by the opening ‘$\,[\,$’ in interval notation. However, $\,5\,$ is not in the domain of the function, indicated by the closing ‘$\,)\,$’ in interval notation. just ‘collapse’ each point, in its own ‘vertical channel’, into the $\,x\,$axis. 
Now consider the same graph again, but this time focusing attention on the outputs, which are the [beautiful math coming... please be patient] $\,y$values of the points. As the point $\,P\,$ is moved through the entire graph, all the $\,y$values indicated in red are taken on. These are the outputs for this function, as the inputs vary through the entire domain. Therefore, the range of this function is the interval $\,[0,5)\,$. Notice that $\,0\,$ is in the range of the function, indicated by the opening ‘$\,[\,$’ in interval notation. However, $\,5\,$ is not in the range of the function, indicated by the closing ‘$\,)\,$’ in interval notation. just ‘collapse’ each point, in its own ‘horizontal channel’, into the $\,y\,$axis. 
Each function is now discussed in detail, indicating important properties that you must know.
Read the discussion of the identity function carefully; it introduces notation that is
not repeated for the subsequent basic models.
THE RECIPROCAL FUNCTION,
[beautiful math coming... please be patient]
$\,\displaystyle f(x)=\frac{1}{x}$
righthand end behavior: as [beautiful math coming... please be patient] $\,x \rightarrow \infty\,$, $\,y\rightarrow 0$ lefthand end behavior: as $\,x \rightarrow \infty\,$, $\,y\rightarrow 0$ Behavior Near Zero: righthand behavior near zero: as [beautiful math coming... please be patient] $\,x \rightarrow 0^{+}\,$, $y\rightarrow\infty$ The sentence ‘$\ x\rightarrow 0^{+}\ $’ is read aloud as: $\,x\,$ approaches zero from the righthand side This means that the inputs are getting arbitrarily close to zero, coming in from the positive ($\,+\,$) side. lefthand behavior near zero: as [beautiful math coming... please be patient] $\,x \rightarrow 0^{}\,$, $y\rightarrow \infty$ The sentence ‘$\ x\rightarrow 0^{}\ $’ is read aloud as: $\,x\,$ approaches zero from the lefthand side This means that the inputs are getting arbitrarily close to zero, coming in from the negative ($\,\,$) side. 

On this exercise, you will not key in your answer. However, you can check to see if your answer is correct. 
PROBLEM TYPES:
