Polynomial Functions

Starting with

moves the parabola by units to the right.

Similarly moves the parabola by units to the left.

Hence the correct answer is option .

First, we need to get this function into a more standard form.

Now we can see that while the function is being horizontally compressed by a factor of 2, it's being translated 3 units to the right, not 6. (It's also being vertically stretched by a factor of 4, of course.)

Starting with

moves the parabola by units to the right.

Similarly moves the parabola by units to the left.

Hence the correct answer is option .

First, we need to get this function into a more standard form.

Now we can see that while the function is being horizontally compressed by a factor of 2, it's being translated 3 units to the right, not 6. (It's also being vertically stretched by a factor of 4, of course.)

When solving functions within functions, we begin with the innermost function and work our way outwards. Therefore:

and

When solving functions within functions, we begin with the innermost function and work our way outwards. Therefore:

and

This problem relies on our knowledge of a radical expression equal to . The functions are subbed into one another in order from most inner to most outer function.

and

This problem relies on our knowledge of a radical expression equal to . The functions are subbed into one another in order from most inner to most outer function.

and

To transform a function horizontally, we must add or subtract the units we transform to x directly. To move left, we add units to x, which is opposite what one thinks should happen, but keep in mind that to move left is to be more negative. To flip a function, the entire function changes in sign.

After making both of these changes, we get

We will need to determine the equation of the parabola in standard form, which is:

Use the FOIL method to expand the binomials.

Shifting this up two units will add two to the value of .

The answer is: