Question

Where does the graph of f(x) = 4√2x - 1 + 3 start?OA. (1,-4)OB. (-1,4)Oc. (-1,-4)OD. (1,3)

Answer 1

Given: A function-

`f(x)=4√(2x-1)+3`

Required: To determine the point where the function starts.

Explanation: To determine where the function starts, we need to determine the domain and range of the function. The domain of a function is the set of x values for which the function is defined.

The square root is not defined for negative values. Hence the domain of the function is the set of all x values greater than or equal to zero as follows-

`\begin{gathered} √(2x-1)\ge0 \\ 2x\ge1 \\ x\ge(1)/(2) \\ Domain=[(1)/(2),\infty) \end{gathered}`

And the range for a function of the type-

`c√(ax+b)+k`

is-

`f(x)\ge k`

Hence, the range of the function is-

`[3,\infty)`

Hence, the function starts at the point (1/2,3).

Final Answer: Option D is correct.