### About One-to-One Function Algebraic Method:

We already learned that a one-to-one function occurs when for each x, there is only one y and for each y, there is only one x. So now we can use this definition to develop a simple test. If f(a) = f(b), this implies that a = b, if the function is one-to-one. So what we can do is plug in an a for x and plug in a b for x and set these two equal to each other. If it turns out that we end up with a = b, then the function is one-to-one.

Test Objectives
• Demonstrate an understanding of the definition of a one-to-one function
• Demonstrate the ability to determine if a function is one-to-one using an algebraic method
One-to-One Function Algebraic Method Practice Test:

#1:

Instructions: determine if the function is one-to-one.

$$a)\hspace{.2em}f(x)=\sqrt{x + 2}- 1$$

#2:

Instructions: determine if the function is one-to-one.

$$a)\hspace{.2em}f(x) = x^2 - 8$$

#3:

Instructions: determine if the function is one-to-one.

$$a)\hspace{.2em}f(x)=|x - 1|$$

#4:

Instructions: determine if the function is one-to-one.

$$a)\hspace{.2em}f(x)=\frac{1}{x - 8}$$

#5:

Instructions: determine if the function is one-to-one.

$$a)\hspace{.2em}f(x)=-\sqrt{25 - x^2}$$

Written Solutions:

#1:

Solutions:

a) This function is one-to-one.

#2:

Solutions:

a) This function is not one-to-one.

#3:

Solutions:

a) This function is not one-to-one.

#4:

Solutions:

a) This function is one-to-one.

#5:

Solutions:

a) This function is not one-to-one.