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1 answer:
Answer:
see attached
Step-by-step explanation:
<h3>1.</h3>Solid dots go at all the end points except the one at (3, 6), which gets an open dot signifying the function is not defined for that point.
For the first portion of the graph, the square root function is shifted left one unit and scaled vertically by a factor of 3.
The second portion of the graph is a line with a slope of -1. It would have a y-intercept of 5 if it were defined there. It has an x-intercept of 5.
<h3>2.</h3>The y-intercept is found by setting x=0 and solving for y.
... y = log(2·0+1) -1 = log(1) -1 = 0 -1 = -1
The x-intercept is found by setting y=0 and solving for x.
... 0 = log(2x +1) -1
... 1 = log(2x +1) . . . add 1
... 10 = 2x +1 . . . . . . take the antilog
... x = (10 -1)/2 = 4.5 . . . . . subtract 1, divide by the x coefficient
The intercepts are (0, -1) and (4.5, 0).
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The domain and range of the graph of a logarithmic function are;
- Domain; 0 < x < +∞
- Range; The set of real numbers.
The basic equation of a logarithmic function can be presented in the form;
Where;
b > 0, and b ≠ 1, given that we have;
The inverse of the logarithmic function is the exponential function presented as follows;
Given that <em>b</em> > 0, we have;
Therefore, the graph of a logarithmic function has only positive x-values
The graph of a logarithmic function is one with a domain and range defined as follows;
Domain; 0 < x < +∞
Range; -∞ < y < +∞, which is the set of real numbers.
The correct option therefore has a domain as <em>x </em>> 0 and range as the set of all real numbers.
Learn more about finding the graphs of logarithmic functions here:
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The answer is y=3 ....
