Answer:
Step-by-step explanation:
A geometric series is one where each term is multiplied by a constant value known as r to get the next term
Sum of n terms of a geometric series is
Sum of infinite series is obtained as the limiting value of this sum when n tends to infinity
We find that only when |r|<1, r power n tends to 0 as n tends to infinity.
Other r power n diverges.
Hence geometric series infinite sum formula is valid only when
|r|<1 since the series sum converges to a finite value
Answer:
g(x) = -Ix - 4I + 1
Step-by-step explanation:
* Lets revise some transformation
- If the function f(x) translated horizontally to the right by h units, then
the new function g(x) = f(x - h)
- If the function f(x) translated horizontally to the left by h units, then
the new function g(x) = f(x + h)
- If the function f(x) translated vertically up by k units, then the new
function g(x) = f(x) + k
- If the function f(x) translated vertically down by k units, then the
new function g(x) = f(x) – k
- A vertical stretching is the stretching of the graph away from the
x-axis
- If k > 1, the graph of y = k • f(x) is the graph of f(x) vertically
stretched by multiplying each of its y-coordinates by k.
- A vertical compression is the squeezing of the graph toward
the x-axis.
- If 0 < k < 1 (a fraction), the graph of y = k • f(x) is the graph of f(x)
vertically compressed by multiplying each of its y-coordinates by k.
- If k should be negative, the vertical stretch or compress is followed
by a reflection across the x-axis.
* Lets solve the problem
∵ The graph of f(x) represented by the function f(x) = -2Ix - 4I + 2
∵ The y-intercept of f(x) is -6 and y-intercept of g(x) is -3
∵ -3/-6 = 1/2
∴ We will multiply f(x) by 1/2 to get the y-intercept of g(x)
- That means f(x) is compressed vertically by scale factor 1/2 to be g(x)
∴ g(x) = 1/2 [ -2Ix - 4I + 2]
∴ g(x) = -Ix - 4I + 1
- To be sure from the answer check the point (4 , 2) in f(x), when
we multiply the y-coordinate by 1/2 the point change to (4 , 1)
which is belong to g(x) that means f(x) translate 1 unit down to be
g(x)
∴ g(x) = -Ix - 4I + 1
