The input variables in the logarithmic functions are the same as the
base raised to the power of the output of the function.
Responses:
1. The x-intercept is the point is at the point (-4, 0)
The y-intercept is at the point (0, -1)
The vertical asymptote is the line, x ≈ -5
2. The x-intercept is the point (-3, 0)
3. The domain is; (0, ∞)
The range is; (-∞, ∞)
4. A shift of -3 units (3 units reduction in f(x) values)
5.
<h3>How can the logarithmic functions be analyzed?</h3>
1. The intercepts of the graphs are the point the graph crosses the axes;
The x-intercept is the pint the graph crosses the x-axis, and where, y = 0
- From the graph, the x-intercept is the point where x = -4, which is the point
The y-intercept is the point the graph crosses the y-axis, and where, x = 0
- From the graph, the y-intercept is the point where y = -1, which is the point
The asymptote are the lines the graph approaches but never reaches.
- The vertical asymptote is the line<u>, x ≈ -5</u>
2. The x-intercept of g(x) = log (x + 4) is given as follows;
At the x-intercept, we have;
g(x) = 0 = log (x + 4)
Which gives;
1 = x + 4
x = 1 - 4 = -3
- The x-intercept is the point where, x = -3, which is the point
3. The domain are the possible x-values
The given logarithmic function is f(x) = log₅(x)
The minimum value of x is approximately 0, the maximum value is ∞
Therefore;
- The domain is;
Similarly
- The range is;
4. f(x) = log x
g(x) = log(x) - 3
Therefore; g(x) = f(x) - 3
- The transformation that is needed to produce g(x) from f(x) is a vertical shift down of 3 units.
5. From the graph, we have;
f(x) = log (x)
The asymptote of g(x) is the line x = -1
At points x - 1, g(x) is f(x) + 4
Therefore;
Learn more about logarithmic functions here:
brainly.com/question/3314861