Question

NEED URGENTLY WILL GIVE BRAINLIEST TYSM

Answer 1

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. $\underline{g(x) = log(x + 1) + 4}$

How can the logarithmic functions be analyzed?

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 $\underline{(-4, \ 0)}$

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 $\underline{(0 \ -1)}$

The asymptote are the lines the graph approaches but never reaches.

• The vertical asymptote is the line, x ≈ -5

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 $\underline{(-3, \ 0)}$

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; $\underline{(0, \ \infty)}$

Similarly

• The range is; $\underline{(-\infty, \ \infty)}$

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;

• $\underline{g(x) = log(x + 1) + 4}$

Learn more about logarithmic functions here:

brainly.com/question/3314861