Exponential functions are related to logarithmic functions in that they are inverse functions. Exponential functions move quickly up towards a [y] infinity, bounded by a vertical asymptote (aka limit), whereas logarithmic functions start quick but then taper out towards an [x] infinity, bounded by a horizontal asymptote (aka limit).
If we use the natural logarithm (ln) as an example, the constant "e" is the base of ln, such that:
ln(x) = y, which is really stating that the base (assumed "e" even though not shown), that:
if we try to solve for y in this form it's nearly impossible, that's why we stick with ln(x) = y
but to find the inverse of the form:
switch the x and y, then solve for y:
So the exponential function is the inverse of the logarithmic one, f(x) = ln x
Answer:
C) Domain is {2}, Range is {2, 3}
Step-by-step explanation:
For one value of x there are two values of y, which contradicts the definition of a function.
Definition of a function:
A function is an equation for which any x that can be plugged into the equation will yield exactly one y out of the equation.
<em>All the other options follow this definition except C</em>
The percent of change would be -33.3% which would then equal a 33.3% decrease (when decimal is rounded)
what I did was turn 1/4 and 1/2 into decimals to make it easier to solve
Using the binomial distribution, it is found that there is a 0.4096 = 40.96% probability that he answers exactly 1 question correctly in the last 4 questions.
<h3>What is the binomial distribution formula?</h3>
The formula is:
The parameters are:
- x is the number of successes.
- n is the number of trials.
- p is the probability of a success on a single trial.
Considering that there are 4 questions, and each has 5 choices, the parameters are given as follows:
n = 4, p = 1/5 = 0.2.
The probability that he answers exactly 1 question correctly in the last 4 questions is P(X = 1), hence:
0.4096 = 40.96% probability that he answers exactly 1 question correctly in the last 4 questions.
More can be learned about the binomial distribution at brainly.com/question/24863377
#SPJ1
Perpendicular line always have slopes that are negative reciprocals of one another. Mathematically,
m1*m2=-1
So to be perpendicular to the line given, let's rearrange it to the point slope form of a line...
3y=6x ?3 (not sure what you wanted to type there)
anyway isolating y by dividing both side by three will leave 2x where 2 is the slope.
So for the other line to be perpendicular, m*2=-1, m=-1/2, now we have:
y=-x/2 +b, we can now you the point given to solve for b
4=-2/2 +b
4=-1+b
b=5 so
y=-x/2 +5 or more neatly
y=(10-x)/2
