Question

Which function represents shifting d(x)=3x+4−−−−−√+2 left by 6 units?(1 point) Responses g(x)=3x+10−−−−−−√+2 g left parenthesis x right parenthesis equals 3 Start Root x plus 10 End Root plus 2 j(x)=3x+4−−−−−√−4 j left parenthesis x right parenthesis equals 3 Start Root x plus 4 End Root minus 4 h(x)=3x+4−−−−−√+8 h left parenthesis x right parenthesis equals 3 Start Root x plus 4 End Root plus 8 f(x)=3x−2−−−−−√+2

Answer 1

To shift the function \( d(x) = \sqrt{3x + 4} + 2 \) left by 6 units, you need to replace \( x \) with \( x + 6 \) in the function.

So, the new function \( g(x) \) after the shift would be:

\[
g(x) = \sqrt{3(x + 6) + 4} + 2
\]

Now, let's simplify this:

\[
g(x) = \sqrt{3x + 18 + 4} + 2
\]

\[
g(x) = \sqrt{3x + 22} + 2
\]

Now, looking at the options provided:

- \( g(x) = \sqrt{3x + 10} + 2 \) (incorrect)
- \( j(x) = \sqrt{3x + 4} - 4 \) (incorrect)
- \( h(x) = \sqrt{3x + 4} + 8 \) (incorrect)
- \( f(x) = \sqrt{3x - 2} + 2 \) (incorrect)

None of the provided functions match \( g(x) = \sqrt{3x + 22} + 2 \). However, based on the function definition for shifting left by 6 units, you should check if the first option \( g(x) = \sqrt{3x + 10} + 2 \) could be a simplification mistake, but it does not correctly represent shifting left by 6 units.

Thus, the function representation for shifting \( d(x) \) left by 6 units is:
\[
g(x) = \sqrt{3x + 22} + 2
\]
And none of the provided options are correct.