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The use of graphs to determine if an equation represents a function, and discusses how to extract valuable information such as intercepts, domain, range, and symmetry from the graphs. It includes examples and instructions on how to find intercepts algebraically and test for symmetry.
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How do we use the graph of an equation to see if it is a function?
Ex. 𝑦 = 𝑥ଷ^ 𝑓(𝑥) = 𝑥ଷ^ 𝑥𝑦 = 1 𝑓(𝑥) = ଵ ௫ Not a function because f(1)=1 and -1. *Functions work like the graphs if the function value f(x) is your y.
What values are on the x- and y-axis? What are their equations? x-axis: y-axis:
Ex. 2 𝑥 + 3𝑦 = 6
Test for symmetry:
Ex. 2 𝑥 + 3𝑦 = 6 Ex. 9 𝑥ଶ^ + 4𝑦 = 36
Ex. 𝑦 = 𝑥ଷ^ − 27
If we have the graphs, we can get all this information directly! Ex. Let f be the function whose graph is shown. (a) What are f(1), f(0), and f(4)?
(b) What is the domain of f?
(c) What is the range of f? (d) List the intercepts.
(e) For what values of x does f (x) = – 3? (f) For what values of x is f (x) > 0?
