Express the function graphed on the axes below as a piecewise function.
1 answer:
Answer:
f(x) = {x-3 for x ≤ -1; -3x+14 for x > 5}
Step-by-step explanation:
To write the piecewise function, we can consider the pieces one at a time. For each, we need to define the domain, and the functional relation.
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<h3>Left Piece</h3>The domain is the horizontal extent. It is shown as -∞ to -1, with -1 included.
The relation has a slope (rise/run) of +1, and would intersect the y-axis at -3 if it were extended.
The first piece can be written ...
f(x) = x-3 for x ≤ -1
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<h3>Right Piece</h3>The domain is shown as 5 to ∞, with 5<em> not included</em>.
The relation is shown as having a slope (rise/run) of (-3)/(1) = -3. If extended, it would intersect the point (5, -1), so we can write the point-slope equation as ...
y -(-1) = -3(x -5)
y = -3x +15 -1 = -3x +14
The second piece can be written ...
f(x) = -3x +14 for x > 5
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<h3>Whole function</h3>Putting these pieces together, we have ...
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<em>Additional comment</em>
Sometimes it is convenient to write inequalities in number-line order (using < or ≤ symbols). This gives a visual indication of where the variable stands in relation to the limit(s). Perhaps a more conventional way to write the domain for the second piece is, <em>x > 5</em>.
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Answer:
Step-by-step explanation:
Hello!
The objective of this exercise is to compare the "Churn rate" between the two major cell phone providers in colorado springs.
For each provider, the number of subscribers was noted at the beginning and end of a month.
The study variables are:
X₁: Number of customers that cut ties with HTC over a month.
X₂: Number of customers that cut ties with Mountain Communications over a month.
To compare the churn rate of both companies, the parameters of interest are the population proportions of customers that stopped using the companies services over the given period.
The hypotheses of interest are:
H₀: p₁ = p₂
H₁: p₁ ≠ p₂
α: 0.01
The statistic to use is the standard normal approximation:
Z≈N(0;1)
HTC
n₁= 10000 customers (beginning of the month)
x₁= 190 customers (people that stopped using the company service)
sample proportion 'p₁= x₁/n₁= 190/10000= 0.019
Mountain Communications
n₂= 12285 customers (beginning of the month)
x₂= 215 customers (people that stopped using the company service)
sample proportion 'p₂= x₂/n₂= 215/12285= 0.0175
pooled sample proportion
'p= 0.0182
The p-value for this test is: 0 .4048
Note: Using the p-value method to decide over a hypothesis test, the decision rule is:
If p-value ≥ α, then you do not reject the null hypothesis.
If p-value < α, then you reject the null hypothesis.
The p-value < α, so the decision is to reject the null hypothesis.
With a significance level of 1%, there is enough evidence to conclude that there is a difference between the churn rate of the two cell phone providers.
I hope it helps!