Replace the values of $h$ and $k$ to create the equation of the transformed function.
$g(x)=\sqrt{x+h}+k$
Answer (2)
Choose values for h and k : Let h = 2 and k = 3 .
Substitute the chosen values into the equation: g ( x ) = x + 2 + 3 .
The transformed function is: g ( x ) = x + 2 + 3 .
Explanation
Understanding the Problem The problem asks us to replace the values of h and k in the function g ( x ) = x + h + k . The table provided is irrelevant. We can choose any values for h and k to create a transformed function. Let's choose h = 2 and k = 3 .
Substituting the Values Now, we substitute h = 2 and k = 3 into the equation g ( x ) = x + h + k . This gives us:
g ( x ) = x + 2 + 3
Writing the Resulting Equation The resulting equation is g ( x ) = x + 2 + 3 . This represents a transformation of the basic square root function, where the graph is shifted 2 units to the left and 3 units upward.
Examples
Imagine you are designing a water fountain where the height of the water stream follows a square root function. By adjusting the parameters h and k , you can control the horizontal shift and vertical height of the water stream. For example, if h is positive, the stream starts further away, and if k is positive, the stream is lifted higher. This allows you to customize the fountain's appearance to fit your design.
To create the transformed function g ( x ) = x + h + k , choose values for h and k , such as h = − 4 and k = 5 . Substituting these values results in g ( x ) = x − 4 + 5 , indicating a shift of 4 units to the right and 5 units upward. Adjusting h and k allows for various transformations of the square root function.
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