Question

Select the correct function which corresponds to the following graph: (0,0.5)

Answer 1

Answer:
`The\text{ correct function is f\lparen x\rparen= 2}^(x-1)\text{ \lparen option B\rparen}`Step-by-step explanation:

Given:

An exponential graph with a given point (0, 0.5)

To find:

the function that corresponds to the graph

To determine the correct function, we will substitute x in each of the functions with the x coordinate of the given point and compare the result with the y coordinate of the given point.

`\begin{gathered} for\text{ point: \lparen0, 0.5\rparen: } \\ x\text{ = 0, y = f\lparen x\rparen = 0.5} \\ \\ a)\text{ f\lparen x\rparen = 2}*2^(x-1) \\ when\text{ x = 0} \\ f(x)\text{ = 2}*2^(0-1)\text{ = 2}*2^(-1) \\ f(x)\text{ = 2}*(1)/(2)\text{ = 1} \\ This\text{ is different from the f\lparen x\rparen value of the given point} \end{gathered}`
`\begin{gathered} b)\text{ f\lparen x\rparen= 2}^(x-1) \\ f(x)\text{ = 2}^(0-1)\text{ = 2}^(-1) \\ f(x)\text{ = }(1)/(2)\text{ = 0.5} \\ This\text{ is the same as the f\lparen x\rparen value of the given point} \end{gathered}`
`\begin{gathered} c)\text{ f\lparen x\rparen = 2}*2^x \\ f(x)\text{ = 2}*2^0\text{ = 2}*1 \\ f(x)\text{ = 2} \\ This\text{ is different from the f\lparen x\rparen value of the given point} \end{gathered}`
`\begin{gathered} d)\text{ f\lparen x\rparen= 2}^x \\ f(x)\text{ = 2}^0\text{ = 1} \\ This\text{ is different from the f\lparen x\rparen value of the given point} \end{gathered}`
`\begin{gathered} e)\text{ f\lparen x\rparen= 2}^(x+1) \\ f(x)\text{ = 2}^(0+1)\text{ = 2}^1 \\ f(x)\text{ = 2} \\ This\text{ is different from the f\lparen x\rparen value of the given point} \end{gathered}`

Hence, the correct function that represents the graph is f(x) = 2^(x-1)