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How do you graph #g(x) = | 2x - 7 | #?

Answer 1

Draw the half-line #y = g(x) = 2x-7, above ( 7/2, 0 )# and construct its mirror image with respect to #x = 7/2#, to form the V-shape graph of #y = 2x-7#-

#g(x) >= 0#, for all x. #g(7/2) = 0#.. For #x < 7/2, g(x) = 7 - 2x#

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Answer 2

Nathan Axel

To graph the function g(x) = |2x - 7|, follow these steps:

Identify key points:
- Find the x-intercept by setting g(x) = 0 and solving for x.
- Find the vertex by setting the expression inside the absolute value equal to 0 and solving for x.
Plot the key points on a coordinate plane.
Determine the behavior of the graph:
- For x < 7/2, g(x) = 7 - 2x.
- For x > 7/2, g(x) = 2x - 7.
Draw straight line segments connecting the points to create the graph.
The graph will be V-shaped, with the vertex at (7/2, 0) and the arms extending upward and downward from the vertex.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.