Question

Which of the following is true? 1) the horizontal line test is used to determine if a function's inverse ill be a function 2) in an inverse relation, coordinates of the ordered pairs are multiplied by 2, 3) an inverse of a function is always a function

Answer 1

The true statement within the given options is that the horizontal line test is used to determine if a function's inverse will be a function. The other statements about inverse relations and function inversions are incorrect.

Step-by-step explanation:

The first statement, "the horizontal line test is used to determine if a function's inverse will be a function," is correct. This test involves drawing horizontal lines through the graph of the original function; if any horizontal line intersects the graph more than once, then the function does not have an inverse that is also a function.

The second and third statements are incorrect. An inverse relation does not necessarily involve multiplying coordinates of ordered pairs by any factor; instead, it involves switching the x and y coordinates. Additionally, the inverse of a function is not always a function; it must pass the horizontal line test to be considered a function.