Question

Which equation represents the transformed function below?

On a coordinate plane, a parent function starts at (0, negative 1) and then curves up into quadrant 1 and approaches y = 1. A transformed function starts at (0, 4) and then curves up into quadrant 1 and approaches y = 6.

_____ = parent function; y = log x
- - - - - = transformed function
y = log x + 5
y = log x minus 5
y = log (x + 5)
y = log (x minus 5)

Answer 1

The equation that represents the transformed function is y = log(x) + 5.
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Answer 2

The transformed function is described by the equation y = log x + 5, which indicates the parent function y = log x has been shifted upward by 5 units.

Step-by-step explanation:

To determine which equation represents the transformed function, we need to understand how transformations to logarithmic functions affect their graphs. From the description, we know that the parent function is y = log x, which has a horizontal asymptote at y = -1. The transformed function starts at the point (0, 4) and approaches a horizontal asymptote at y = 6. This means the entire graph has been shifted upward by 5 units.

The correct transformation of the parent function to achieve this outcome would be to add 5 to the function value, resulting in y = log x + 5. The option 'y = log x minus 5' would shift the graph down, and the options that involve changing the argument of the logarithm (e.g., 'y = log (x + 5)') would horizontally shift the graph, not vertically as described.