True or False.
1. Every function is a relation.
2. When you switch the inputs and outputs of any function, the resulting relation is a function.
I suppose a function is a relation
However if you switch inputs and outputs of a function (take the inverse) you may not get a function. For example y = sin x is a function. There is a y for every x. However for any y between -1 and + 1 there are an infinite number of x values, so if you input x = 0 for example you get y =0, pi (180 deg), 2 pi, 3 pi, etc
1. True. Every function is a relation because a function is a specific type of relation in which each input is associated with exactly one output.
2. False. When you switch the inputs and outputs of a function, the resulting relation may not necessarily be a function. In a function, each input has a unique output, but when you switch them, there may be multiple inputs with the same output, which violates the definition of a function. So, in general, switching inputs and outputs does not guarantee that the resulting relation will be a function. It could be a function, but it's not always the case. It's like switching the ingredients and the recipe for a dish – you might end up with something completely different, or inedible!
1. True. Every function is a relation because a function is a special type of relation where each input value has exactly one corresponding output value.
2. False. When you switch the inputs and outputs of a function, the resulting relation may not always be a function. For a relation to be a function, each input value must have only one corresponding output value. If switching the inputs and outputs results in any input value having multiple corresponding output values, then the resulting relation is not a function.
1. True. Every function is a relation. In mathematics, a relation is defined as a set of ordered pairs consisting of inputs and corresponding outputs. A function is a specific type of relation where each input has only one unique output. So, any function qualifies as a relation.
2. False. When you switch the inputs and outputs of any function, the resulting relation may or may not be a function. This concept is known as the inverse relation. While some functions have inverse relations that are also functions, not all functions satisfy this condition. To determine whether the inverse of a function is also a function, you need to check if each output has only one corresponding input in the inverse relation.