what is the range of this logarithmic function?\n$ - 7,\\infty )$\n$( - 7,\\infty )$
what is the range of this logarithmic function?\n$ - 7,\\infty )$\n$( - 7,\\infty )$
Answer
Explanation:
Step1: Recall the range property of logarithmic functions
The range of a basic logarithmic function (y = \log_a(x)) ((a>0,a\neq1)) is ((-\infty,\infty)). Transformations (horizontal shifts, vertical shifts, reflections, stretches, and compressions) do not change the range of a logarithmic function.
Step2: Analyze the given graph
Looking at the (y -)values of the graph, as (x) approaches the vertical asymptote (from the right) and as (x) moves to the right - hand side of the graph, the (y -)values can take any real number. There is no restriction on the (y -)values.
Answer:
The range of the logarithmic function is ((-\infty,\infty))