Using the stated transformation, the graph of g(2x) is given at the end of the answer.
<h3>Horizontal stretch and compression</h3>
An horizontal stretch or an horizontal compression happens when a constant is multiplied at the domain of the function, as follows:
g(x) = f(ax).
The definition of stretch or compression depends on the value of the constant a, as follows:
- If a > 1, it is a compression by a factor of 1/a.
- If a < 1, it is a stretch by a factor of 1/a.
In this problem, the rule is:
f(x) = g(2x).
Meaning that f(x) is an horizontal compression by a factor of 1/2 of g(x), and then the vertices are given as follows:
That is, in each vertex, the x-coordinate was divided by 2, and thus the graph with these vertices is given at the end of the answer.
More can be learned about transformations at brainly.com/question/28725644
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Answer: number of years that it will take for the balance to reach $120,000 is 42 years
Step-by-step explanation:
Initial amount deposited into the account is $4000. This means that the principal is $4000
P = 4000
It was compounded annually. This means that it was compounded once in a year. So
n = 1
The rate at which the principal was compounded is 8.4%. So
r = 8.4/100 = 0.084
Let the number of years that it will take for the balance to reach $120,000. It means that it was compounded for a total of t years.
Amount, A at the end of t years is $120,000
The formula for compound interest is
A = P(1+r/n)^nt
120000 = 4000(1 + 0.084/1)^1×t
120000/4000 = 1.084^t
30 = 1.084^t
t = 42 years
Answer:
p = 10t - 100
Step-by-step explanation:
Perform the indicated multiplication: p = 10t - 100.