Use the graph of y = f(x) to graph each function g.

g(x) = f(x)+1

검증된 단계별 안내

Identify the original function f(x) from the graph. Here, f(x) is a horizontal line segment from (1, -3) to (4, -3).

Understand the transformation for g(x) = f(x) + 1. This means you add 1 to every y-value of f(x).

Apply the transformation to the endpoints of the line segment: For (1, -3), calculate the new y-value as -3 + 1.

Similarly, for (4, -3), calculate the new y-value as -3 + 1.

Plot the new points with the updated y-values and draw a horizontal line segment connecting them to graph g(x).

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주요 개념

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Function Transformation - Vertical Shift

A vertical shift moves the graph of a function up or down without changing its shape. Adding a constant to the function, as in g(x) = f(x) + 1, shifts the entire graph of f(x) upward by that constant value. For example, if f(x) = -3, then g(x) = -3 + 1 = -2.

Graphing Piecewise or Segment Functions

When graphing functions defined on specific intervals, such as a line segment from (1, -3) to (4, -3), it is important to only plot points within the given domain. The graph of g(x) = f(x) + 1 will maintain the same domain but shift the y-values accordingly.

Coordinate Points and Plotting

Understanding how to plot points on the coordinate plane is essential. Each point (x, y) represents a location where x is the horizontal position and y is the vertical position. For g(x) = f(x) + 1, each y-coordinate of f(x) is increased by 1, so points like (1, -3) become (1, -2).

Use the graph of y = f(x) to graph each function g.g(x) = f(x)+1