The graph of h(x) = f(x + 1) is f(x) shifted one unit left, maintaining the same slope and shape.
The graph h(x) using the function f(x) = -2x, we need to understand that h(x) is a transformation of f(x) involving a horizontal shift.
Starting with f(x) = -2x, when we introduce h(x) = f(x + 1), the "+1" inside the function indicates a shift to the left by 1 unit. This transformation implies that whatever f(x) was at x, h(x) will now be at x - 1. For example, f(0) is at x = 0, but h(0) will be at x = -1 because of the shift.
The function h(x) = f(x + 1) moves the graph of f(x) one unit to the left. When graphing h(x), the original function f(x) = -2x remains the same in shape but shifts horizontally by one unit in the negative x-direction.
The graph of f(x) = -2x is a straight line passing through the origin with a slope of -2. When we shift this graph one unit to the left, every point on the graph of f(x) will move one unit to the left.
So, the graph of h(x) = f(x + 1) will be the graph of f(x) = -2x shifted one unit to the left. It maintains the same slope and shape but appears shifted to the left by one unit along the x-axis.