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Friday 19th of January
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# Graphing Functions

Functions can be expressed in a variety of ways, including using words, algebraic equations, tables, and graphs.

Tables and graphs are often used to make it easier to visualize how the input and the output are related.

Procedure â€” To Graph a Function

Step 1 Make a table of ordered pairs that satisfy the function.

Step 2 Plot the ordered pairs on a Cartesian coordinate system.

Step 3 Connect the plotted points with a smooth line.

Example

Graph the function: f(x) = x2 - 4x - 2

Solution

Step 1 Make a table of ordered pairs. We can select any values we want for x and then calculate the corresponding values for f(x). We will let x = -2, 0, 2, 4, and 6.

 x f(x) = x2 - 4x - 2 (x, y) -2 0 2 46 f(-2) = (-2)2 - 4(-2) - 2 = 4 + 8 - 2 = 10 f(0) = (0)2 - 4(0) - 2 = 0 - 0 - 2 = -2 f(2) = (2)2 - 4(2) - 2 = 4 - 8 - 2 = -6 f(4) = (4)2 - 4(4) - 2 = 16 - 16 - 2 = -2 f(6) = (6)2 - 4(6) - 2 = 36 - 24 - 2 = 10 (-2, 10)(0, -2) (2, -6) (4, -2)(6, 10)

Step 2 Plot the ordered pairs.

Step 3 Connect the plotted points.

Note:

When we say â€œconnect the plotted pointsâ€ we mean to draw a smooth line between them, and also to continue the line past the end points.

That is, the graph should not stop at the plotted end points; it should continue past those points following the pattern of the graph.