Questions: Begin by graphing f(x)=log5 x. Then use transformations of this graph to graph the given function. What is the vertical asymptote? Use the graphs to determine the given function's domain and range. h(x)=4+log5 x Determine the transformations that are needed to go from f(x)=log5 x to the given graph. Choose the correct answer below. A. The graph of f(x)=log5 x should be shifted 4 units to the right. B. The graph of f(x)=log5 x should be shifted 4 units to the left. C. The graph of f(x)=log5 x should be shifted 4 units downward. D. The graph of f(x)=log5 x should be shifted 4 units upward.

Solution Steps

The function \( f(x) = \log_{5} x \) is a logarithmic function with base 5.

The vertical asymptote of \( f(x) = \log_{5} x \) is \( x = 0 \). Since \( h(x) = 4 + \log_{5} x \) is a vertical shift of \( f(x) \), the vertical asymptote remains \( x = 0 \).

The domain of \( f(x) = \log_{5} x \) is \( (0, \infty) \). Since \( h(x) = 4 + \log_{5} x \) is a vertical shift, the domain remains \( (0, \infty) \).

The range of \( f(x) = \log_{5} x \) is \( (-\infty, \infty) \). Since \( h(x) = 4 + \log_{5} x \) is a vertical shift by 4 units upward, the range of \( h(x) \) is also \( (-\infty, \infty) \).

The transformation needed to go from \( f(x) = \log_{5} x \) to \( h(x) = 4 + \log_{5} x \) is a vertical shift of 4 units upward.

Final Answer