Question

Given the functions f(x)=1x−2+1 and g(x)=1x+5+9 .

Which statement describes the transformation of the graph of function f onto the graph of function g?




The graph shifts 8 units left and 7 units up.

The graph shifts 8 units right and 7 units down.

The graph shifts 7 units left and 8 units up.

The graph shifts 7 units right and 8 units down.

Answer 1

For this problem you would look at the difference between the two equations. Left and right is determined by the -2 and the +5 in the problems, to get from -2 to +5, you would add 7 but (and i dont really know how to explain the reasoning for this) whenever this number is positive, it goes left and whenever it is negative, it goes right. Figuring out if it shifts up or down is the same, look at the numbers +1 and +9 in the equations. If you go from +1 to +9, you would be adding 8, and this makes it shift upward.

Therefore the answer is the third one: the graph shifts 7 units left and 8 units up

Answer 2

We want to see which transformation we must apply to f(x) to get g(x). We will see that the correct option is the third one: "The graph shifts 7 units left and 8 units up."

First, let's describe the transformations used in this problem:

Vertical shift:

For a function f(x) we define a vertical shift of N units as:

g(x) = f(x) + N

• If N is positive the shift is up
• If N is negative the shift is down.

Horizontal shift:

For a function f(x) we define an horizontal shift as:

g(x) = f(x + N)

• If N is positive the shift is to the left
• If N is negative the shift is to the right.

Now we can just compare the two functions:

$f(x) = \frac{1}{x - 2} + 1\\\\\\g(x) = \frac{1}{x + 5} + 9$

Now we can write g(x) as:

$g(x) = \frac{1}{x - 2 + 7} + 1 + 8 = f(x + 7) + 8$

So this is a shift of 7 units to the left and 8 units up.

The correct option is:

"The graph shifts 7 units left and 8 units up."

If you want to learn more about shifts, you can read:

https://brainly.com/question/23381749