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Sagot :
To plot the points for the inverse of the given function, you need to switch the [tex]\( x \)[/tex] values with their corresponding [tex]\( f(x) \)[/tex] values. This means that the [tex]\( x \)[/tex]-coordinates from the original function become the [tex]\( y \)[/tex]-coordinates in the inverse function, and vice versa. Let's do this step-by-step:
1. Let's list out the values from the table and what they will be in the inverse:
- For [tex]\( x = -4 \)[/tex] and [tex]\( f(x) = 9 \)[/tex], the inverse point will be [tex]\( (9, -4) \)[/tex].
- For [tex]\( x = 0 \)[/tex] and [tex]\( f(x) = 5 \)[/tex], the inverse point will be [tex]\( (5, 0) \)[/tex].
- For [tex]\( x = 3 \)[/tex] and [tex]\( f(x) = 2 \)[/tex], the inverse point will be [tex]\( (2, 3) \)[/tex].
- For [tex]\( x = 7 \)[/tex] and [tex]\( f(x) = -2 \)[/tex], the inverse point will be [tex]\( (-2, 7) \)[/tex].
2. Now, we plot these points on a graph where the x-axis represents the new inverse x-values (which were originally f(x) values) and the y-axis represents the new inverse y-values (which were originally x-values):
- Plot the point [tex]\( (9, -4) \)[/tex].
- Plot the point [tex]\( (5, 0) \)[/tex].
- Plot the point [tex]\( (2, 3) \)[/tex].
- Plot the point [tex]\( (-2, 7) \)[/tex].
To plot these points, follow these steps:
- Start at the origin [tex]\((0, 0)\)[/tex].
- Move to the [tex]\( x \)[/tex]-coordinate of the point.
- From there, move to the [tex]\( y \)[/tex]-coordinate of the point.
For example:
- For the point [tex]\( (9, -4) \)[/tex], start at [tex]\((0, 0)\)[/tex], move 9 units to the right along the [tex]\( x \)[/tex]-axis, then move 4 units down along the [tex]\( y \)[/tex]-axis.
- For the point [tex]\( (5, 0) \)[/tex], start at [tex]\((0, 0)\)[/tex], move 5 units to the right along the [tex]\( x \)[/tex]-axis, and stay at the same level on the [tex]\( y \)[/tex]-axis.
- For the point [tex]\( (2, 3) \)[/tex], start at [tex]\((0, 0)\)[/tex], move 2 units to the right along the [tex]\( x \)[/tex]-axis, then move 3 units up along the [tex]\( y \)[/tex]-axis.
- For the point [tex]\( (-2, 7) \)[/tex], start at [tex]\((0, 0)\)[/tex], move 2 units to the left along the [tex]\( x \)[/tex]-axis, then move 7 units up along the [tex]\( y \)[/tex]-axis.
By following these steps, you will have successfully plotted the points for the inverse of the function.
1. Let's list out the values from the table and what they will be in the inverse:
- For [tex]\( x = -4 \)[/tex] and [tex]\( f(x) = 9 \)[/tex], the inverse point will be [tex]\( (9, -4) \)[/tex].
- For [tex]\( x = 0 \)[/tex] and [tex]\( f(x) = 5 \)[/tex], the inverse point will be [tex]\( (5, 0) \)[/tex].
- For [tex]\( x = 3 \)[/tex] and [tex]\( f(x) = 2 \)[/tex], the inverse point will be [tex]\( (2, 3) \)[/tex].
- For [tex]\( x = 7 \)[/tex] and [tex]\( f(x) = -2 \)[/tex], the inverse point will be [tex]\( (-2, 7) \)[/tex].
2. Now, we plot these points on a graph where the x-axis represents the new inverse x-values (which were originally f(x) values) and the y-axis represents the new inverse y-values (which were originally x-values):
- Plot the point [tex]\( (9, -4) \)[/tex].
- Plot the point [tex]\( (5, 0) \)[/tex].
- Plot the point [tex]\( (2, 3) \)[/tex].
- Plot the point [tex]\( (-2, 7) \)[/tex].
To plot these points, follow these steps:
- Start at the origin [tex]\((0, 0)\)[/tex].
- Move to the [tex]\( x \)[/tex]-coordinate of the point.
- From there, move to the [tex]\( y \)[/tex]-coordinate of the point.
For example:
- For the point [tex]\( (9, -4) \)[/tex], start at [tex]\((0, 0)\)[/tex], move 9 units to the right along the [tex]\( x \)[/tex]-axis, then move 4 units down along the [tex]\( y \)[/tex]-axis.
- For the point [tex]\( (5, 0) \)[/tex], start at [tex]\((0, 0)\)[/tex], move 5 units to the right along the [tex]\( x \)[/tex]-axis, and stay at the same level on the [tex]\( y \)[/tex]-axis.
- For the point [tex]\( (2, 3) \)[/tex], start at [tex]\((0, 0)\)[/tex], move 2 units to the right along the [tex]\( x \)[/tex]-axis, then move 3 units up along the [tex]\( y \)[/tex]-axis.
- For the point [tex]\( (-2, 7) \)[/tex], start at [tex]\((0, 0)\)[/tex], move 2 units to the left along the [tex]\( x \)[/tex]-axis, then move 7 units up along the [tex]\( y \)[/tex]-axis.
By following these steps, you will have successfully plotted the points for the inverse of the function.
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