Question

vertical dilation by a factor of (1)/(3), reflection over the x axis, horizontal translation right 8, vertical translation down 3

Answer 1

To perform the given transformations on a graph, you need to follow a specific order. The given transformations include a vertical dilation by a factor of 1/3, reflection over the x-axis, horizontal translation right by 8 units, and vertical translation down by 3 units.

Step-by-step explanation:

To perform the given transformations on a graph, you need to follow a specific order. The given transformations include a vertical dilation by a factor of 1/3, reflection over the x-axis, horizontal translation right by 8 units, and vertical translation down by 3 units.

1. Start by applying the vertical dilation. Multiply the y-values of each point on the graph by 1/3.
2. Next, apply the reflection over the x-axis. Change the sign of each y-value on the graph.
3. Then, perform the horizontal translation by adding 8 to each x-value on the graph.
4. Finally, apply the vertical translation by subtracting 3 to each y-value on the graph.

Follow these steps in order to apply the given transformations correctly.

The complete question is:vertical dilation by a factor of (1)/(3), reflection over the x axis, horizontal translation right 8, vertical translation down 3

Answer 2

The given transformations, you need to multiply the function by 1/3 for vertical dilation, reflect over the x-axis by negating the function, translate it right 8 by replacing x with x - 8, and translate it down 3 by subtracting 3 from the entire function. The final transformed function would be -((1/3)f(x - 8) - 3).

Let's apply these transformations to a generic function f(x).

Vertical dilation by a factor of 1/3: Multiply the function by 1/3. New function: g(x) = (1/3)f(x).

Reflection over the x-axis: Negate the entire function. New function: h(x) = -g(x).

Horizontal translation right 8: Replace x with x - 8. New function: j(x) = h(x - 8).

Vertical translation down 3: Subtract 3 from the entire function. New function: k(x) = j(x) - 3.

So, if you have an original function f(x), the final transformed function k(x) incorporating all these transformations would be: k(x) = -((1/3)f(x - 8) - 3).