Question

Please see the question below. Please answer in full. Thanks in advance.

Answer 1

2) (-4, ∞)

3) X-Intercept: -2; Y-Intercept: 1

4) The graph of y =
`log_(2)`(x + 4) - 1 is translated 4 units to the left compared to its parent function.

Explanation:

2)

To find the domain, find the value of x where g(x) will be undefined:

x = -4

This is because the logarithm of 0 is undefined. So, this means that anything greater than -4 will be part of the function:

(-4, ∞)

3)

First, to find the y-intercept, set x to 0:

g(x) = (4) - 1

Then, simplify this:

g(x) = 2 - 1

g(x) = 1

Then, to find the x-intercept, set y to 0:

0 =
`log_(2)`(x + 4) - 1

Simplify:

`log_(2)`(x + 4) = 1

To solve for x, use the logarithmic definition: If
`log_(a)`(b) = c then b = :

x + 4 =
`2^(1)`

x = -2

4)

The graph of y =
`log_(2)`(x + 4) - 1 is translated 4 units to the left compared to its parent function. The graph moved 4 units to the left.

Answer 2

y = log base (x - h) + k

1) Vertical Asymptote: -4

The vertical asymptote is at -4 because when dealing with logs, the vertical asymptote will always be the h value, and since in the original equation you are subtracting it from x, you flip the sign, so instead of positive 4, you get negative 4.

2) Domain: x > -4

When graphing a logarithm, it doesn't cross the vertical asymptote, and it is a positive function, so all of the x values will be greater than -4.

3) X and Y Intercepts: x = -2, y = 1

To find the x-intercept, y has to equal 0, so plug 0 in for y and solve for x. To find the y-intercept, x has to equal 0, so plug in 0 for x and solve for y.

4) Transformations: shifted 4 units to the left, and shifted 1 unit up.

To find the horizontal movement, look at h. If h is positive, then the function has been shifted that many units to the left. If h is negative, then the function has been shifted that many units to the right, To find the vertical movement, look at k. If k is positive, then the function has moved that many units up. If k is negative, then the function has moved that many units down.