Question

The function f(x) goes through the point (-2,6). which of the following translation of f(x) will go through the point (3,5)?

option 1; f(x-5)+1
option 2; f(x+5)-1
option 3; f(x-5)-1
option 4; f(x+5)+1

Answer 1

Option 3: the function that goes through the point (3, 5) is f(x-5)-1

Explanation:

To find which function goes through the point (3, 5), we can substitute 3 for x and solve for the value of f(x).

For option 1, f(x-5)+1, we have:

f(3-5)+1 = f(-2)+1 = 6+1 = 7

For option 2, f(x+5)-1, we have:

f(3+5)-1 = f(8)-1 = ?

For option 3, f(x-5)-1, we have:

f(3-5)-1 = f(-2)-1 = 6-1 = 5

For option 4, f(x+5)+1, we have:

f(3+5)+1 = f(8)+1 = ?