Can someone tell me if I have this one correct.
log_1/2x 2+log_1/2x
the relationship is a shift of 1 unit horizontally
if g(x) = f(x)+2,
the graph is shifted up 2 units
f(x-1) is f(x) shifted right by 1.
Find the slope-intercept equation of the line perpendicular to line 4x-y=20 and containing the point (16,-7).
x is at lest 9 what is x
To determine if you have the relationship correct, we need to first understand what the function log_1/2x represents.
The expression log_1/2x refers to the logarithm function with a base of 1/2 and an argument of x. The logarithm function represents the power to which the base must be raised to obtain the argument. In this case, we have a logarithm function with a base of 1/2.
Now let's analyze the expression:
log_1/2x + 2 + log_1/2x
Since both terms have the same base (1/2), we can combine them using the properties of logarithms:
log_1/2x + log_1/2x + 2
Using the logarithmic identity log_a(x) + log_a(y) = log_a(xy), we can simplify further:
log_1/2(x * x) + 2
Simplifying x * x, we get:
log_1/2(x^2) + 2
Now, the expression represents a logarithm with a base of 1/2 and an argument of x^2, plus 2.
To determine if there is a horizontal shift in the function, we need to compare it to the standard form of a logarithmic function: log_a(x - h), where a represents the base and h represents the horizontal shift.
In our case, the base a is 1/2, and the argument is x^2. There is no subtraction or addition operation present in the argument, so there is no horizontal shift in the function.
In conclusion, your expression log_1/2x + 2 + log_1/2x represents a logarithm with a base of 1/2 and an argument of x^2, plus 2. It does not exhibit a horizontal shift.