Graphing Functions – Practice Problems

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Graphing functions is pretty much the same as graphing equations, with the symbol f(x) being a fancy way of writing y. To graph a function f(x), follow the following steps:

(1) Pick some values for x.
(2) Substitute in each value of x into f(x); the result will be the y value of the x which was plugged in.
(3) Plot the resulting ordered pairs (x,y) in the plane.
(4) If the equation is linear, connect the points with a line, otherwise connect the points with a smooth curve.

The domain (i.e. the x values) gives the vertical projection of the graph, whereas the range (i.e. the y values) gives the horizontal projection of the graph.

To determine if the graph is a function or not, we use the vertical line test: if any vertical line touches only one point of the graph, then the graph represents a function; this means graphically that every x is assigned to exactly one y. Otherwise, the graph does not represent a function.

Analyze functions using different representations.

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Exercises in this Practice Problem
Describe how the given graph represents a function.
Decide which graphs represent functions.
Complete the function table for the function $y=2x^2+3$.
Decide which stars belong to the graph of the function.
Explain how to draw the graph of the function $y=2x+8$.
Match the graph with its corresponding function.