What are the key features of logarithmic and exponential graphs?
The exponential function, is formally known as the real function ex, where e is Euler's number, approximately 2.71828; this function has as a domain of definition the set of real numbers, and has the peculiarity that its derivative is the same function.
The logarithm, on the other hand, is the inverse function of the exponential.
how do transformations affect them?
Let's see this question with two examples
logarithm
f (x) = lnx original function
f (x) = - lnx reflection in x axis
f (x) = ln (x-2) displacement two units to the right.
f (x) = 2 + lnx displacement two units up
f (x) = ln (-x) refect in axis y
f (x) = ln (2-x) displacement two units to the right, reflection y
f (x) = - ln (-x) reflection in x, and in y axis
Exponential
f (x) = 5 ^ x original function.
f (x) = - 5 ^ x reflection on x axis
f (x) = 5 ^ -x reflection in axis y
f (x) = 5 ^ (x + 3) horizontal displacement 3 units to the left
f (x) = 5 ^ x +3 vertical displacement 3 units towards the top
f (x) = 5 ^ (x + 1) -4 displacement 1 unit to the left and 4 units to the bottom.
Answer:
x + y =2
-x -x
y = -1x + 2
Perpendicular is y= 1x + 2
Step-by-step explanation:
Answer:
1763
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Step-by-step explanation:
The answer is 9x^3-6x^2+3x
We can rearrange the initial equation to y=mx+b
y=2x-5
Since perpendicular slopes must equal -1,
x=the perpendicular slope
2x=-1
x=-1/2
(Or you can just take the negative reciprocal above is just the "formula form" for it)
Therefore, the perpendicular slope is -1/2
