Answer:
Let's define two transformations.
Vertical translation.
If we have a function f(x), a vertical translation of N untis is written as:
g(x) = f(x) + N
If N is positive, then the translation is upwards
If N is negative, then the translation is downwards.
Horizontal translation.
If we have a function f(x), a horizontal translation of N units is written as:
g(x) = f(x - N)
if N is positive, then the translation is to the right
If N is negative, then the translation is to the left.
Now we have a function g(x) that is a transformation of a parent function f(x) (we actually do not know which parent function, so i assume f(x) = x^2) such that we have a shift right 5 units and up 3 units.
Then:
g(x) = f(x - 5) + 3
and again, using f(x) = x^2
g(x) = (x - 5)^2 + 3
Answer:
1.09
Step-by-step explanation:
I *really* wish I had work to show, but I just used a calculator as it is a simple division problem. Since you can do long divison, here are the steps! It is very hard to show on here, so I have typed it out:
Step 1: Estimate the answer by rounding. You'll use this estimate to check your answer later.
Step 2: If the divisor is not a whole number, then move the decimal place n places to the right to make it a whole number. Then move the decimal place in the dividend the same number of places to the right (adding some extra zeros if necessary.)
Step 3: Divide as usual. If the divisor doesn't go in evenly, add zeros to the right of the dividend and keep dividing until you get a 0 remainder, or until a repeating pattern shows up.
Step 4: Put the decimal point in the quotient directly above where the decimal point now is in the dividend.
Step 5: Check your answer against your estimate to see if it's reasonable.
It is
log 39=2
Explanation:
By definition the logarithmic form
log bx=y is equivalent to the exponential form
by=x
Hence from the given 32=9 you have b=3 , y=2 , x=9
hence the logarithmic form is
log 3 9=2
We want our exponential function to look like
y = ab^x.
Let a = the initial y-value.
Our initial value is the first number given for f(x). So, a = 3.
Let b = the number that is needed to go from 3 to 6 to 12 to 24 to 48.
We find b by division.
So, b = the next number divided by the previous.
So, b = 6/3 = 2.
We now plug in our values into the general formula above.
y = ab^x
Answer: y = (3)(2)^x
