Question

Let f(x) = |x| for all real numbers x. Write the formula for the function represented by the described

transformation of the graph of y = f(x).
b. First, a vertical stretch with scale factor 3 is performed, then a reflection over the xx-axis, then a translation left
4 units, and finally a translation up 5 units.

Answer 1

Answer: Hello there!

we have the function f(x) = IxI and we want to write the formula represented by the transformation

"First, a vertical stretch with scale factor 3 is performed, then a reflection over the x-axis, then a translation left

4 units, and finally a translation up 5 units."

first, we have a vertical stretch; this means that we have

y = a*f(x) where a is a real number, in this case, the scale is 3, so we have:

y = 3*f(x) = 3IxI

now we have a reflection over the x-axis

this is equivalent to multiply our function for -1.

y = -1(3f(x)) = -3f(x) = -3IxI

Now a translation left for 4 units, this is equivalent to have the change from x to x + 4; this is

y = f(x + 4)

then our function is:

y = -3f(x+4) = -3I x + 4I

Finally a translation up by 5 units.

For this we need to add to te function a constant equal to 5.

y = f(x) + 5

in our case:

y = -3f(x + 4) + 5 = -3Ix+4I + 5

Then our function after all of these trnasformations is:

f(x) = -3Ix+4I + 5

Answer 2

y = (-3f(x+4))+5

Explanation:

Please see the picture below.

1. Apply to the function the vertical stretch with scale factor 3:

y = 3f(x)

2. Multiply the function by -1 to reflect it over the x-axis:

y = -3f(x)

3. Add up 4 units from x to translate the function 4 units to the left:

y = -3f(x+4)

4. Add up 5 units to the entire function to translate it up 5 units:

y = (-3f(x+4))+5