\(\textbf{1)}\) \(\text{Does this represent a function? } {(1{,}2),(2{,}4),(2{,}5),(5{,}8)} \)
\(\textbf{2)}\) \(\text{Does this represent a function? } {(1{,}2),(2{,}4),(3{,}5),(5{,}8)} \)
\(\textbf{3)}\) \(\text{Does this represent a function? } {(1{,}2),(2{,}2),(2{,}2),(5{,}2)} \)
\(\textbf{4)}\) \(\text{Does this represent a function? } {(1{,}2),(1{,}4),(1{,}5),(1{,}8)} \)
\(\textbf{5)}\) \(\text{Does this represent a function? } {(1{,}1),(2{,}2),(3{,}3),(5{,}5)} \)
\(\textbf{6)}\) \(\text{Does this represent a function? }\)
| \(0\) | \(1\) | \(2\) | \(3\) | |
| \(4\) | \(7\) | \(10\) | \(13\) |
\(\textbf{11)}\) Does this represent a function?
\(\textbf{12)}\) Does this represent a function?
See Related Pages\(\)
\(\bullet\text{ Is it linear?}\)
\(\,\,\,\,\,\,\,\,y=mx+b\)
\(\bullet\text{ Evaluating Functions}\)
\(\,\,\,\,\,\,\,\,f(x)=5x+3,\,\text{find } f(3)\)
\(\bullet\text{ Composite Functions}\)
\(\,\,\,\,\,\,\,\,(f\circ g)(x)=f(g(x))\)
\(\bullet\text{ Inverse Functions and Relations}\)
\(\,\,\,\,\,\,\,\,f^{-1}(x)=\frac{x+3}{2}\)
\(\bullet\text{ Operations of Functions}\)
\(\,\,\,\,\,\,\,\,(f+g)(3)=f(3)+g(3)\)
In Summary
There are several ways to determine whether a given relation is a function. One way is to use the vertical line test, which involves drawing a vertical line on the graph of the relation and observing the number of times that the line intersects the graph. If the line intersects the graph in exactly one point for every value of the input, then the relation is a function.
Another way to determine whether a relation is a function is to examine its mathematical definition. A function is a relation that assigns exactly one output value to each input value. Therefore, if a relation is defined by an equation or set of equations that uniquely determines the output value for every possible input value, then the relation is a function.