Question

Analyze the graphs g(x)=−4x+1−−−−√+3.5
and h(x)=−4x+1−−−−√−4.5
. Which option correctly describes the transformation to take g(x)
to h(x)
? (1 point)
Responses

vertical translation up 8 units
vertical translation up 8 units

vertical translation down 8 units
vertical translation down 8 units

vertical translation down 7 units
vertical translation down 7 units

vertical translation right 8 units

Answer 1

To analyze the graphs of the functions \( g(x) = -\sqrt{-4x + 1} + 3.5 \) and \( h(x) = -\sqrt{-4x + 1} - 4.5 \), we can compare the two equations to determine how \( g(x) \) transforms into \( h(x) \).

The only difference between \( g(x) \) and \( h(x) \) is the constant term at the end:

- In \( g(x) \), the constant term is \( +3.5 \).
- In \( h(x) \), the constant term is \( -4.5 \).

To determine the vertical transformation, we can find the difference between the two constants:

\[
3.5 - (-4.5) = 3.5 + 4.5 = 8
\]

Since \( h(x) \) is obtained by subtracting 8 from \( g(x) \), it means that \( h(x) \) is \( g(x) \) shifted downward by 8 units.

Thus, the correct option is:

**vertical translation down 8 units**.