QuestionIdentify which of these are functions: $f(x)=|x-5|$ and the set $\{(-5,6),(-2,8),(0,4),(8,8)\}$ .

Studdy Solution

STEP 1

Assumptions1. A function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. . The vertical line test can be used to determine if a graph represents a function. If any vertical line intersects the graph more than once, then the graph does not represent a function.
3. The given relations are $f(x)=|x-5|$ and $\{(-5,6),(-,8),(0,4),(8,8)\}$ .

STEP 2

Let's first consider $f(x)=|x-5|$ . The absolute value function is a function because for every input $x$ , there is exactly one output $f(x)$ .

STEP 3

Now let's consider the set of ordered pairs $\{(-5,6),(-2,8),(0,),(8,8)\}$ . To determine if this set represents a function, we need to check if each input (the first number in each pair) is related to exactly one output (the second number in each pair).

STEP 4

Looking at the set of ordered pairs, we see that each input is paired with exactly one output. Therefore, this set also represents a function.
So, both $f(x)=|x-|$ and $\{(-,6),(-2,8),(0,4),(8,8)\}$ represent functions.

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