Math Problem Statement
Begin by graphing f left parenthesis x right parenthesis equals log Subscript 3 Baseline 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. g left parenthesis x right parenthesis equals log Subscript 3 Baseline left parenthesis x plus 2 right parenthesis Question content area bottom left Part 1 Graph the function g left parenthesis x right parenthesis equals log Subscript 3 Baseline left parenthesis x plus 2 right parenthesis . Graph the asymptote of g(x) as a dashed line. Use the graphing tool to graph the function. Part 2 What is the vertical asymptote of g(x)? enter your response here (Type an equation.) Part 3 What is the domain of g left parenthesis x right parenthesis equals log Subscript 3 Baseline left parenthesis x plus 2 right parenthesis ? enter your response here (Simplify your answer. Type your answer in interval notation.) Part 4 What is the range of g left parenthesis x right parenthesis equals log Subscript 3 Baseline left parenthesis x plus 2 right parenthesis ? enter your response here (Simplify your answer. Type your answer in interval notation.)
Solution
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Math Problem Analysis
Mathematical Concepts
Logarithmic Functions
Function Transformations
Graphing Logarithmic Functions
Formulas
f(x) = log_3(x)
g(x) = log_3(x + 2)
Theorems
Transformation of functions
Domain and range of logarithmic functions
Suitable Grade Level
Grades 10-12
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