The graph of h(x) is a vertical translation of the graph of g(x) down 3 units, as h(x) = g(x) - 3 indicates a downward shift. The correct answer is A.
The function h(x) = g(x) - 3 represents a vertical translation of the graph of g(x) downward by 3 units. This is because subtracting 3 from g(x) shifts every point on the graph of g(x) downward by 3 units. In the original function g(x) = -1/2x + 6, the slope is -1/2, indicating a negative slope, and the y-intercept is 6.
When we subtract 3 from g(x) to form h(x), the entire graph shifts downward while maintaining the same slope. Option A correctly describes this vertical translation, specifying that h(x) is a downward shift. Options B, C, and D describe translations in the wrong direction (upward or horizontally) and with incorrect magnitudes (3 units instead of -3 units). Therefore, the accurate description is that the graph of h(x) is a vertical translation of g(x) down 3 units. The correct answer is A.
Que. Let g(x)= -1/2x+6 and h(x)= g(x)-3
which statement described the graph of h(x)?
A. the graph of h (x) is a vertical translation of the graph of g(x) down 3 units
B. the graph of h(x) is a vertical translation of the graph of g(x) Up 3 units
C. the graph of h(g) x is horizontal translation of of the graph of g(x) left 3 units
D. the graph of h(x) is a horizontal translation of the graph of g(x) write 3 in it