Determine whether or not the function is one-to-one.
1. f(x) = 2x - 7
2. f(x) =(11x − 5)
Both of your equations are linear functions, and their graphs are straight lines.
All straight line graphs, unless they are vertical lines, are functions.
So they are one-to-one
To determine whether a function is one-to-one, we need to check if different inputs (x-values) produce different outputs (y-values).
1. For the function f(x) = 2x - 7, let's assume that we have two different inputs, a and b, such that f(a) = f(b). This means that 2a - 7 = 2b - 7. By simplifying this equation, we get 2a = 2b, which implies a = b. This shows that the function is one-to-one since different inputs will always produce different outputs.
2. For the function f(x) = 11x - 5, let's again assume we have two different inputs, a and b, such that f(a) = f(b). This means that 11a - 5 = 11b - 5. Simplifying this equation, we get 11a = 11b, which implies a = b. This shows that the function is also one-to-one since different inputs will always produce different outputs.
Therefore, both functions f(x) = 2x - 7 and f(x) = 11x - 5 are one-to-one.