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A function is given by a table of values, a graph, a formula, or a verbal description.

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A function is given by a table of values, a graph, a formula, or a verbal description. Determine whether it is one-to-one.

g(x) =1/x
asked Jan 26, 2015 in CALCULUS by anonymous
edited Jan 29, 2015 by bradely

1 Answer

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Step 1:

The rational function image.

image

Graph the function image.

The rational function graph is two or more parts.

Graph the above function using asymptotes and some coordinate pairs.

Step 2:

image

Find the asymptotes.

Find the vertical asymptote by equating denominator to zero.

image is the vertical asymptote.

Since the degree of the numerator is less than the degree of the denominator, horizontal asymptote is image.

Choose random values for image and find the corresponding values for image.

image image image
image image image
image image image
image image image
image image image

Graph:

Draw the coordinate plane.

Plot the asymptotes and points found in the table.

Draw horizontal test line image.

Observe the graph: the horizontal line image touches the graph of the function exactly one point.

Therefore, the function is one-to-one.

Solution:

image is one-to-one function.

answered Jan 31, 2015 by david Expert
edited Jan 31, 2015 by david

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