Question

G of X equals -1/2 X +6 and H of X equal G of X -3 which statement describes the graph of each of X

Answer 1

The correct description of h(x) is h(x) =
`2^x`−1. Option C is the right choice.

Option (A), h(x) =
`-2^x,` would reflect the graph of f(x) across the x-axis. This means that the points would be mirrored across the x-axis. However, the graph of h(x) shown in the image does not match this reflection.

Option (B), h(x) =
`-2^{-x` , would reflect the graph of f(x) across the y-axis and then flip it horizontally. This means that the points would be mirrored across the y-axis and then swapped left and right. However, the graph of h(x) shown in the image does not match this transformation either.

Option (C), h(x) =
`2^x`−1, would shift the graph of f(x) downward by one unit. This means that all the points on the graph of f(x) would be moved one unit down. The graph of h(x) shown in the image does appear to be shifted down by one unit from the graph of f(x), so this option could be a possibility.

Option (D), h(x) =
`2^(-x)` , would reflect the graph of f(x) across the y-axis. This means that the points would be mirrored across the y-axis. The graph of h(x) shown in the image does appear to be a reflection of the graph of f(x) across the y-axis, so this option is also a possibility.

Therefore, the two options that could potentially describe the graph of h(x) are (C) and (D). To determine which one is correct, we can notice that the graph of h(x) passes through the point (0,1).

The graph of f(x) also passes through this point, and if we reflect the graph of f(x) across the y-axis, the resulting graph would pass through the point (0,−1), not (0,1).

However, if we shift the graph of f(x) down by one unit, the resulting graph would pass through the point (0,1).

Therefore, the correct answer is Option (C), h(x) =
`2^x`−1.

In conclusion, the graph of h(x) is obtained by shifting the graph of f(x) downward by one unit.