Question

Which function represents shifting h(x)=53x−−√+10
ℎ
(
𝑥
)
=
5
3
𝑥
+
10
down 6 units?(1 point)
Responses

k(x)=53x−−√−6
𝑘
(
𝑥
)
=
5
3
𝑥
−
6
k times x is equal to 5 square root of 3 x minus 6

g(x)=53x−6−−−−−√
𝑔
(
𝑥
)
=
5
3
𝑥
−
6
g of x is equal to 5 square root of 3 x minus 6 end root

m(x)=53x−−√+4
𝑚
(
𝑥
)
=
5
3
𝑥
+
4
m times x is equal to 5 square root of 3 x plus 4

p(x)=53x−−√+16

Answer 1

To shift a function down by a certain number of units, you subtract that number from the function's output.

Given the function \( h(x) = 5\sqrt{3x} + 10 \), to shift it down by 6 units, you would subtract 6 from the entire function:

\[
k(x) = h(x) - 6 = 5\sqrt{3x} + 10 - 6
\]
\[
k(x) = 5\sqrt{3x} + 4
\]

Thus, the correct representation of shifting \( h(x) \) down by 6 units is:

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

This means the correct choice from your options is:

**m(x) = 5√(3x) + 4**.