I need help with two problems. Any help is appreciated. I will give best and answer and 10 points to the first person to get them right. Thanks!!!
1. Using complete sentences, explain the characteristics and parts of a logarithmic function and
its graph.
2.Using complete sentences, explain the similarities and differences between the graphs of a radical function and a logarithmic function.
1. Using complete sentences, explain the characteristics and parts of a logarithmic function and
its graph.
2.Using complete sentences, explain the similarities and differences between the graphs of a radical function and a logarithmic function.
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differences
Range of radical function = [0, infinity)
Range of logarithmic function = (-infinity, infinity) and graph of logarithmic function has 1 vertical asymptote
y = sqrtx and y = ln x
both are increasing functions and similar domain
The logarithmic function is defined as the inverse of the exponential function.
For B > 0 and B not equal to 1,
y = Log Bx is equivalent to x = B y.
characteristic:
Such logarithmic graphs of the form have certain characteristics in common
• graph crosses the x-axis at (1, 0)
• when b > 1, the graph increases
• when 0 < b < 1, the graph decreases
• the domain is all positive real numbers (never zero)
• the range is all real numbers
• graph passes the vertical line test - it is a function
• graph passes the horizontal line test - its inverse is also a function.
• graph is asymptotic to the y-axis - gets very, very close to the y-axis but does not touch it or cross it.
Range of radical function = [0, infinity)
Range of logarithmic function = (-infinity, infinity) and graph of logarithmic function has 1 vertical asymptote
y = sqrtx and y = ln x
both are increasing functions and similar domain
The logarithmic function is defined as the inverse of the exponential function.
For B > 0 and B not equal to 1,
y = Log Bx is equivalent to x = B y.
characteristic:
Such logarithmic graphs of the form have certain characteristics in common
• graph crosses the x-axis at (1, 0)
• when b > 1, the graph increases
• when 0 < b < 1, the graph decreases
• the domain is all positive real numbers (never zero)
• the range is all real numbers
• graph passes the vertical line test - it is a function
• graph passes the horizontal line test - its inverse is also a function.
• graph is asymptotic to the y-axis - gets very, very close to the y-axis but does not touch it or cross it.