Question

Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used. Consider the graph of the function f(x)=1n x . Match each transformation of function f with a feature of the transformed function vertical asymptote of x=0 x-intercept at (1.5,0) function decreases as x increases y-intercept at (0,-1/2)

Answer 1

Transformations of the function f(x) = ln(x) can result in features such as a vertical asymptote at x=0, an x-intercept at a certain point, and adjustments to the increasing or decreasing nature of the function. A y-intercept at (0,-1/2) is not possible for this function as ln(x) is undefined at x=0.

Step-by-step explanation:

The transformation of the function f(x) = ln(x) can lead to different features depending on the type of transformation applied. To match each transformation with a feature of the transformed function, consider the following:

• Vertical asymptote of x=0: This is a feature of the original function f(x) = ln(x), as the function is undefined at x=0, creating a vertical asymptote there.
• x-intercept at (1.5,0): To have an x-intercept at (1.5,0), the function would need to be shifted or transformed so that f(1.5)=0 which implies ln(1.5) + some constant = 0. This might hint at a vertical translation.
• Function decreases as x increases: The natural logarithm function naturally increases as x increases, so a transformation that causes it to decrease may involve reflecting it across the y-axis.
• y-intercept at (0,-1/2): This is not possible for the function f(x) = ln(x) as ln(x) is undefined at x=0. Therefore, this feature does not correspond to a transformation of f(x) = ln(x).