Question

Determine if the function f(x)=2x+5 is a one-to-one function.

a) Yes
b) No
c) Cannot be determined
d) Depends on the domain and range

Answer 1

Option A. The function f(x)=2x+5 is a one-to-one function because it passes the Horizontal Line Test, as it is a straight line with a non-zero slope, meaning each x value maps to a unique y value.

Step-by-step explanation:

The student has asked whether the function f(x)=2x+5 is a one-to-one function. A one-to-one function, also known as an injective function, has the property that each element of the domain is mapped to a unique element of the range. This means that for every value of x, there is a distinct value of f(x).

To determine if a function is one-to-one, you can use the Horizontal Line Test. If any horizontal line intersects the graph of the function at more than one point, the function is not one-to-one. However, in the case of the linear function f(x)=2x+5, no horizontal line will cross the graph more than once. This is because it is a straight line with a non-zero slope.

Therefore, the function f(x)=2x+5 is indeed a one-to-one function. The correct answer is:

• (a) Yes