For the graph of the function f,
(a) Find the domain and the range of f.
(b) Find the intercepts.
(c) Is the graph of f symmetric with respect to the x-axis, the y-axis, or the origin?
(d) Find f (2).
(e) For what value(s) of x is ?
(f) Solve .
(g) Graph .
(h) Graph .
(i) Graph .
(j) Is f even, odd, or neither?
(k) Find the interval(s) on which f is increasing.
(a) The domain of f is and the range is
(b) The intercepts are
(c) The x coordinates of the corresponding pairs are symmetric with respect to the y-axis, so the f is symmetric with respect to the y-axis.
(e) The values of x are
(g) The graph is
(h) The graph is
(i) The graph is
(j) The function f is even
(k) The function f is increasing
For the graph of the function f.
The domain is a set of the numbers x for which the function is defined.
The range is a set of all the values of the function,
To find the intercept, check where the graph of the function f intersects the x-axis and the y--axis.
The intercepts are
To find if the graph of f is symmetric with respect to the x-axis, the y-axis, or the origin check the different values of x, the function has the same value,
We can notice that the x- coordinate of the corresponding pairs is symmetric with respect to the y-axis, so the f is symmetric with respect to the y-axis.
To find the value of find the value of the function if
As per the graph, we can notice that the solution are:
To find the values of x when the values of the function are less than zero, we have to find where is the graph of the function f under x-axis.
As per the graph
If a constant k is added to the function, then there will be a vertical shift in the graph that is .
If then the graph will move k unit downwards.
As per the question, we add 2 to the given function, therefore the graph will be
To graph , we must reflect the graph of f along the y-axis.
The graph of f is symmetrical to the y-axis, therefore, the graph of should be the same with f
If a function is multiplied by a scalar factor k, then it will result to a vertical stretch to the graph of the function
if , the graph is stretched vertically or narrow
If the graph is compressed or widens.
If, , the graph is stretched and reflected along the x-axis
if the function is multiplied by positive 2, therefore the graph narrows or stretched vertically
The graph of is
The even functions are symmetric with respect to the y-axis and the odd functions are symmetric with respect to the origin. As per part (c) we have the graph of the f, is symmetric over the y-axis, so the function f is even.
If we increase the value of the argument x, the function values rise. So we have to find those z values.
As per the graph, the f is increasing:
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