The Domain, Range, Vertical Asymptote, And Symmetry Of F(X) = Log₂(X-2)

f(x) = log₂(x-2)

Translate base-2 log right 2

1. What is the domain of the function?

The domain of the function f(x) = log₂(x-2) is all real numbers greater than 2 because the argument of the logarithmic function should be positive.

2. What is the range of the function?

The range of the function f(x) = log₂(x-2) is all real numbers because the logarithmic function can take any real value as its output.

3. What is the vertical asymptote of the function?

The vertical asymptote of the function f(x) = log₂(x-2) occurs when the argument of the logarithmic function is equal to zero. Thus, the vertical asymptote occurs when x = 2.

4. What is the x-intercept of the function?

The x-intercept of a function occurs where the function intersects with the x-axis, which is where the output equals zero. Thus, we set f(x) = 0 and solve for x:

log₂(x-2) = 0
x-2 = 1
x = 3

Therefore, the x-intercept of the function is (3, 0).

5. What is the y-intercept of the function?

The y-intercept of a function occurs where the function intersects with the y-axis, which is where the input equals zero. However, in this case, the function is undefined when x = 0, so there is no y-intercept.

6. Is the function even, odd, or neither?

To determine if the function f(x) = log₂(x-2) is even, odd, or neither, we need to check if it satisfies the following conditions:

– Even: f(-x) = f(x) for all x
– Odd: f(-x) = -f(x) for all x

If the function satisfies the even condition, it is an even function. If it satisfies the odd condition, it is an odd function. If it satisfies neither, it is neither even nor odd.

Let’s check:

f(-x) = log₂(-x-2)

We cannot take the logarithm of a negative number, so f(x) is not defined for negative values of x. Therefore, f(-x) does not equal f(x) for all x, and the function f(x) = log₂(x-2) is neither even nor odd.

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