Identifying Functions (3.6.2)

Question 1

• A function is an equation where you get exactly one result for each value you put in.

Answer 1

• A function is an equation where you get exactly one result for each value you put in.

Question 2

• Vertical line test for a function of x means that for every value of x there exists at most one value of y.

Answer 2

• Vertical line test for a function of x means that for every value of x there exists at most one value of y.

Question 3

For an equation to be a function of x, it must pass the vertical line test. This means that every value of x has no more than one value of y; i.e., a vertical line will intersect a given curve no more than once. In identifying a function, the question is whether for every value of x, there is only one or no values of y. First transform this equation into a statement that shows what y equals in terms of x. Then, you know that this one is a function of x; no matter what you use for x, you will derive only one y. This example meets the function test because, once again, for each value of x you use there will be exactly one value of y. It is easy to check each example using the vertical line test. The first two examples verify graphically what you found out algebraically. They show there is only one y-value for each x-value; i.e., that a vertical line intersects the curve at most once. The third example verifies graphically that the curve fails the vertical line test and, therefore, cannot be considered a function of x.

Answer 3

For an equation to be a function of x, it must pass the vertical line test. This means that every value of x has no more than one value of y; i.e., a vertical line will intersect a given curve no more than once. In identifying a function, the question is whether for every value of x, there is only one or no values of y. First transform this equation into a statement that shows what y equals in terms of x. Then, you know that this one is a function of x; no matter what you use for x, you will derive only one y. This example meets the function test because, once again, for each value of x you use there will be exactly one value of y. It is easy to check each example using the vertical line test. The first two examples verify graphically what you found out algebraically. They show there is only one y-value for each x-value; i.e., that a vertical line intersects the curve at most once. The third example verifies graphically that the curve fails the vertical line test and, therefore, cannot be considered a function of x.