To deal with this item, let us summarize the details of the problem:
(a) Syllabus area: Algebra
(b) Specific topic: Graphical Solutions
For
(i), we should take note that y = f(x).
Since
the given is f(2), then x = 2. This suggest that we should draw the line x = 2
then find the value of y in the intersection of the line x = 2 and the given
graph.
For
(ii), since y = f(x) and the given is f(x) = 0, then y = 0. This means that the
line y = 0 must be drawn. The line y = 0 is also the x-axis. Find the value of
x in the intersection between the x-axis and the given graph.
For
(iii), we are looking for the value of k where there are three solutions. This
means that we are looking for a horizontal line that passes through the given
graph at exactly three points. We should also take note that the value of k is
an integer. The possible values of k are 5, 4, 3, 2, 1, 0, -1, -2, -3, -4, -5
(based on the range of the grid given). Let us draw the horizontal lines and
mark the intersection(s) of each.
Let
us summarize the number of intersections in the following table then determine
the highest value of k where there are three intersections.
For
(iv), to solve for the equation f(x) = x, we should take note that f(x) = y.
Hence, f(x) = x is the same as y = x. By now, you should be familiar with the
graph of this equation. If not, you may use a table to assign values of x then
get the corresponding values of y. The graph is a straight line passing through
the origin and slanting to the right.
Let
us determine the coordinates of the intersection between the line y=x and the
given graph.
Therefore,
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Thank you and God bless!
Thank you and God bless!
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