Question

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

Answer 1

Step 1:

The rational function .

Graph the function .

The rational function graph is two or more parts.

Graph the above function using asymptotes and some coordinate pairs.

Step 2:

Find the asymptotes.

Find the vertical asymptote by equating denominator to zero.

is the vertical asymptote.

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

Choose random values for and find the corresponding values for .

Graph:

Draw the coordinate plane.

Plot the asymptotes and points found in the table.

Draw horizontal test line .

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

Therefore, the function is one-to-one.

Solution:

is one-to-one function.