Questions: The graph of y=g(x) is shown. Draw the graph of y=-g(x).

Transcript text: The graph of $y=g(x)$ is shown. Draw the graph of $y=-g(x)$.

Solution

Solution Steps

Step 1: Identify key points

First, identify some key points on the graph of $y = g(x)$. For example, we can choose the points $(-4, 7)$, $(0, 5)$, $(4, 3)$, and $(7, 6)$.

Step 2: Reflect the points across the x-axis

To obtain the graph of $y = -g(x)$, we reflect each point on the graph of $y = g(x)$ across the x-axis. This means that if $(x, y)$ is a point on the graph of $y = g(x)$, then $(x, -y)$ is a point on the graph of $y = -g(x)$. The reflected points are: $(-4, -7)$ $(0, -5)$ $(4, -3)$ $(7, -6)$

Step 3: Plot the reflected points and draw the graph

Plot the reflected points on the coordinate plane. Then connect these points with line segments to obtain the graph of $y = -g(x)$.

Final Answer The graph of $y = -g(x)$

      y
      ^
      |
  7 -  .       /
      |     /
  6 -  .   /
      |  /
  5 -  . /
      |/
      +----------------> x
      |\\
  -5 -  .\\
      |  \\.
  -6 -  .  \\.
      |    \\.
  -7 -  .    \\.
      |     \\.

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