Question

Which function represents shifting h(x)=53x−−√+10 down 6 units?(1 point) Responses p(x)=53x−−√+16 p left parenthesis x right parenthesis equals 5 Start Root 3 x End Root plus 16 g(x)=53x−6−−−−−−√ g left parenthesis x right parenthesis equals 5 Start Root 3 x minus 6 End Root k(x)=53x−−√−6 k left parenthesis x right parenthesis equals 5 Start Root 3 x End Root minus 6 m(x)=53x−−√+4 m left parenthesis x right parenthesis equals 5 Start Root 3 x End Root plus 4

Answer 1

To shift the function \( h(x) = 5\sqrt{3x} + 10 \) down by 6 units, you need to subtract 6 from the entire function.

So, we have:

\[
h(x) - 6 = 5\sqrt{3x} + 10 - 6
\]

This simplifies to:

\[
h(x) - 6 = 5\sqrt{3x} + 4
\]

Thus, the function that represents shifting \( h(x) \) down by 6 units is:

\[
k(x) = 5\sqrt{3x} + 4
\]

The correct answer is:

**m(x) = 5√(3x) + 4**