Suppose you want to transform the graph of the function into the graph of the function . which transformations should you perform?

A

Step-by-step explanation:

edg2020

A. Reflect the graph of the first function across x-axis, translate it to the left, and translate it 2 units up.

Step-by-step explanation:

We have the original function is .

The new transformed function is given by  .

So, we can see that the following sequence of transformations have been applied to the original function:

1. The function f(x) is reflected about x-axis i.e. f(x) becomes -f(x), which gives

2. This function obtained is translated units to the left i.e.   i.e.

3. Finally, this new function is translated 2 units upwards i.e. i.e.

Hence, after applying, 'reflection across x-axis, translation of to the left, and translation of 2 units up', we get the required function.

the ratio of white tiles to blue tiles is 48: 16. the ratio in it's simplest form is 3: 1.

step-by-step explanation:

ratio: take the first number and add a colon next to it, then add the second number after that. make sure the ratio order matches up with the written problem!

simplest form: we can simplify the ratio 48 : 16 by dividing both terms by the greatest common factor (gcf).

the gcf of 48 and 16 is 16.

divide both terms by 16:

48 ÷ 16 = 3

16 ÷ 16 = 1

reducing to simplest form:

48 : 16 = 3 : 1