1.
"The spending limit on John’s credit card is given by the function f(x)=15,000+1.5x"
means that if the monthly income of John is $ 5,000 ,he can spend at most
f(5,000)=15,000+1.5*5,000=15,000+ 7,500=22, 500 (dollars)
Or for example
if Johns monthly income is $8,000, then he can spend at most
f(8,000)=15,000+1.5*8,000=15,000+ 12,000=27,000 (dollars)
2.
Now, assume that the maximum amount that John can spend is y.
Then, y=15,000+1.5x
we can express x, the monthly income, in terms of y by isolating x:
y=15,000+1.5x
1.5x = y-15,000
X=y-15,000/1.5
thus, in functional notation, x, the monthly income, is a function , say g, of variable y, the max amount:
X=g(y) y-15000/1.5
since we generally use the letter x for the variable of a function, we write g again as:
G (x) x-15000/1.5
tells us that if the maximum amount that John can spend is 50,000 $, then his monthly income is 23,333 $.
3.
If John's limit is $60,000, his monthly income is
G(600,000)=60,000-15,000/ 1.5=45,000/1.5 =30,000
dollars.
Answer: $ 30,000
Remark: g is called the inverse function of f, since it undoes what f does.
instead of g(x), we could use the notation
28.7083333333...
But you could also round it up to 29.
Let's find the derivative of that hyperbola in order to find a slope formula to help us with this equation. We already have an x and y value. The derivative is found this way:
so
. The derivative supplies us with the slope formula we need to write the equation. Sub in the x value of 3 to find what the slope is:
. So in our slope-intercept equation, x = 3, y = 1, and m = -1/3. Use these values to solve for b.
so b = 2. The equation, then, for the line tangent to that hyperbola at that given point is
Answer:The answer is 130
Step-by-step explanation:
Answer:
D. g(x) = (x+ 4)² + 6
Step-by-step explanation:
Here, the given function is f(x) = x²
Now,if a graph x² is translated by (h,k) where:
h = Translation done towards RIGHT
k = Translation done towards UP
Then the translated equation is given as:
y = (x-h)² + k .... (1)
Now here, the graph is translated 6 UNITS UP and 4 UNITS LEFT.
⇒ h = - 4 and k = 6
Substituting the value of h, k in (1) , we get:
g(x) = (x-(-4))² + 6 = (x+ 4)² + 6
⇒ g(x) = (x+ 4)² + 6
Hence, the equation of the translated function, g(x) is g(x) = (x+ 4)² + 6.
