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## Homework Statement

Investigate whether [tex]\psi[/tex](x) = [tex]\phi[/tex](c(x - [tex]\eta[/tex])) & [tex]\psi[/tex](x) = [tex]\phi[/tex](x

^{2}) are test functions.

## Homework Equations

## The Attempt at a Solution

The first function is smooth but has no contact support as it is only 0 at x = [tex]\eta[/tex] so this is not a test function.

The second function is smooth but is not 0 at any interval, so this is not a test function.