Given the following linear function sketch the graph of the function and find the domain and range.
1 answer:
Answer:
see the procedure
Step-by-step explanation:
we have
This is the equation of a line in slope intercept form
where
----> the slope
----> the y-coordinate of y-intercept
To graph the line find out the intercepts
The y-intercept is the point (0,7) ----> given value
The x-intercept is the point (2.33,0) ---> Remember that the x-intercept is the value of x when the value of the function is equal to zero
with the points (0,7) and (2.33,0) sketch the graph
using a graphing tool
Plot the points and join to graph the line
see the attached figure
The domain is all real numbers
The range is all real numbers
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You can use the definition of logarithm and the fact that a positive number raised to any power will always stay bigger than 0.
The domain of the given function is {x | x > 1 and a real number }
The range of the given function is (set of real numbers)
If a is raised to power b is resulted as c, then we can rewrite it that b equals to the logarithm of c with base a.
Or, symbolically:
Since c was the result of a raised to power b, thus, if a was a positive number, then a raised to any power won't go less or equal to zero, thus making c > 0
<h3>How to use this definition to find the domain and range of given function?</h3>Since log(x-1) is with base 10 (when base of log isn't specified, it is assumed to be with base 10) (when log is written ln, it is log with base e =2.71828.... ) thus, we have a = 10 > 0 thus the input x-1 > 0 too.
Or we have:
x > 1 as the restriction.
Thus domain of the given function is {x | x > 1 and a real number }
Now from domain, we have:
(log(x-1) > -infinity since log(0) on right side have arbitrary negatively large value which is denoted by -infinity)
Thus, range of given function is whole real number set (since all finite real numbers are bigger than negative infinity)
Thus, the domain of the given function is {x | x > 1 and a real number }
The range of the given function is (set of real numbers
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