Using translation concepts, it is found that the transformations are as follows:
- In y = -f(x÷2) - 5, the function is reflected over the x-axis, horizontally stretched by a factor of 2 and shifted 5 units down.
- In y = f(-x) + 5, the function is reflected over the y-axis and shifted 5 units up.
What is a translation?
A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
In y = -f(x÷2)-5, we have that:
- f(x) is multiplied by -1, hence it was reflected over the x-axis.
- x is divided by two inside the domain, hence the function was horizontally stretched by a factor of 2.
- 5 is subtracted from f(x), hence the function was shifted 5 units down.
In y = f(-x) + 5, we have that:
- x is multiplied by -1 inside the domain, hence the function was reflected over the y-axis.
- 5 is added to f(x), hence the function was shifted 5 units up.
More can be learned about translation concepts at https://brainly.com/question/4521517
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