The range of h(x) = 1/x

Math Central

Quandaries & Queries

Question from Lucy, a student:

What is the range of the function: h(x)=1/x (and can you please explain why)?

Hi Lucy,

Sketch the graph.

h(x) = 1/x

From the graph it looks like the range of h is all real numbers except zero. Can you prove it?

Suppose that $a$ is a real number and $a \neq 0.$ Can you find a real number $x$ so that $h(x) = a?$

Can you find a real number $x$ so that $h(x) = 0?$ Why not?

Penny

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