Graphs

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Graphs of Functions
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Weve already graphed equations. We can graph
functions in the same way. The thing to remember
is that on the graph the f(x) or function value
is the same as the y value.
If we want to graph the function f (x) 3x 1,
it is the same thing as graphing y 3x 1.
We recognise this as a line with a slope 3 and
y-intercept of -1
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So to graph any functions given, simply write a y
where you see f(x) and then graph with the same
method as you did graphs of equations plugging in
values for x and finding the corresponding y
values and plotting the points. Also recall that
domain is the x-values you can legally plug in
and range is the y-values you get out.
The other thing you need to know is how to tell
from a graph if the graph is of a function or
not. Ill address this on the next screen
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Recall that for a relation to be a function, for
each x there can only be one y value. Lets look
at a couple of graphs.
At x 1 there are two y values.
Look at different x values and see there is only
one y value on the graph for it.
This then is NOT a function
This IS a function
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From what we've just seen, we can tell by looking
at a graph of an equation if it is a function or
not by what we call the vertical line test.
If a vertical line intersects the graph of an
equation more than one time, the equation graphed
is NOT a function.
This is NOT a function
This is a function
This is a function
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Acknowledgement I wish to thank Shawna Haider
from Salt Lake Community College, Utah USA for
her hard work in creating this PowerPoint. www.sl
cc.edu Shawna has kindly given permission for
this resource to be downloaded from
www.mathxtc.com and for it to be modified to suit
the Western Australian Mathematics Curriculum.
Stephen Corcoran Head of Mathematics St
Stephens School Carramar www.ststephens.wa.edu.
au