Answer: [tex]f(x)\text{ = ln0.5x \lparen2nd option\rparen}[/tex]Explanation:
Given:
The graph of a function
To find:
The function represented by the graph
To determine the right function, we will assign values to x in order to get the values of y. Then we will compare the y values with the y values on the graph
let x = 2, 5
[tex]\begin{gathered} when\text{ x = 2} \\ a)\text{ }f(x)=\text{ e}\times0.5x \\ f(x)\text{ = e}\times0.5(2)\text{ = 2.718 \lparen wrong\rparen} \\ \\ b)\text{ }f(x)\text{ = ln0.5x} \\ f(x)\text{ = ln 0.5\lparen2\rparen = 0} \\ \\ c)\text{ }f(x)\text{ = e}^{0.5x} \\ f(x)\text{ = e}^{0.5(2)}\text{ = 2.718 \lparen wrong\rparen} \\ \\ d)\text{ }f(x)\text{ = log0.5x} \\ f(x)\text{ = log0.5\lparen2\rparen = 0} \end{gathered}[/tex]
From the graph: when x = 2, y = 0
This means the likely functions are the 2nd and last option.
We will check for when x = 5 to ascertain the correct function:
[tex]\begin{gathered} f(x)\text{ = ln0.5\lparen5\rparen} \\ f(x)\text{ = 0.916} \\ \\ f(x)\text{ = log0.5\lparen5\rparen} \\ f(x)\text{ = 0.398} \end{gathered}[/tex]
From the graph, the value of y is around 1 when x is 5
Since 0.916 is closer to 1, the function represented by the graph is f(x) ln0.5x
