Find the domain and range of the functions below
1 answer:
Step-by-step explanation:
So let classify each function.
38 is a quadratic because it has a leading variable raised to the 2nd degree.
Quadratics always accept all x values positive or negative so the domain
- All Real Numbers, (- ♾,♾)
Quadratics lowest range is it vertex. The vertex of a typically quadratic is 0 because when we have the function
we have no value after it so 0 is the lowest number.
However we have
So this means that our lowest value will be -9.
We include that point as well. The leading coeffceint is positive so it approach infinity so the range is
- [-9,♾),
39 is a square root function because it has the square root symbol. Remeber that we can't take the square root of a negative number i.e( we can but it isn't graphable on a Cartesian plane). So this means x has to be greater than or equal to zero. We can take the square root of 0.
So set the equation inside the radical equal to zero.
So this means the domain is
- [4,♾)
In a square root function, we restrict our domain to only positive number so the range is
[0,♾)
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Answer:
a. 3x^2 = 81
x^2 = 27
Step-by-step explanation:
Answer:
If we compare the p value and the significance level given we see that
so we can conclude that we have enough evidence to reject the null hypothesis,and we have enough evidence to conclude that the true mean is significantly lower thn 4.8 at 10% of signficance.
Step-by-step explanation:
Data given and notation
represent the sample mean
represent the population standard deviation
sample size
represent the value that we want to test
represent the significance level for the hypothesis test.
z would represent the statistic (variable of interest)
represent the p value for the test (variable of interest)
State the null and alternative hypotheses.
We need to conduct a hypothesis in order to check if thetrue mean is below the specifications, the system of hypothesis would be:
Null hypothesis:
Alternative hypothesis:
If we analyze the size for the sample is > 30 and we know the population deviation so is better apply a z test to compare the actual mean to the reference value, and the statistic is given by:
(1)
z-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".
Calculate the statistic
We can replace in formula (1) the info given like this:
P-value
Since is a one sided test the p value would be:
Conclusion
If we compare the p value and the significance level given we see that
so we can conclude that we have enough evidence to reject the null hypothesis,and we have enough evidence to conclude that the true mean is significantly lower thn 4.8 at 10% of signficance.