Question

A function is transformed into the function

Name the 3 transformations that occurred and describe the general shape of g(x). When describing the shape, you have the option of including a picture of its graph.

A function is transformed into the function

Name the 2 transformations that occurred and describe the general shape of g(x). When describing the shape, you have the option of including a picture of its graph.

Answer 1

Answer:

there will be ni change in shape only position of graph changes

Answer 2

The 3 transformations that occurred and describe the general shape of g(x) are: f(x)->f(x-2), f(x)->3f(x) and f(x)->f(x)+5.

For the second, the two transformations that occurred and describe the general shape of g(x) are:f(x)->-f(x) and f(x)->f(x)-8

In the first part, we see

1. $\\ \sqrt{x}$ change to $\sqrt{x-2}$, which means that f(x) is changed to f(x-2) and hence the graph will be shifted to the left by 2 units.
2. Then, 3 is multiplied to f(x), making it 3f(x), which means the graph is now 3 times bigger.
3. At last, 5 is added to f(x) making it f(x)+5, which would shift the graph to units in the upward direction.

In the second part,

1. f(x) is first converted to -f(x), which means the graph is now a mirror image of its former self along the x axis.
2. Then 8 is subtracted from f(x), making the graph shift 8 units in the negative y axis(downward).