The function g is a transformation of f. If g has a y-intercept at 4, which of the following functions could represent g?
1 answer:
Answer:
g(x) = f(x) - 2
g(x) = f(x + 2)
Step-by-step explanation:
y-intercept of a function:
The y-intercept of a function is the value of y when x = 0.
Function f:
Graph given in this question
When , so the y-intercept is 6.
Additionally, when
If g has a y-intercept at 4, which of the following functions could represent g?
Either we subtract 2 from f, that is:
Or we can also add 2 on the domain, that is, moving 2 units to the right, so:
So the first two options are correct.
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Answer:
(a) -2.8
b) (1) Reject H0: p = 0.50 in favor of HA: p < 0.50; there is sufficient evidence to conclude that less than half of all UGA female students who, if they had a cell phone, would be willing to walk somewhere after dark that they would normally not go.
Step-by-step explanation:
The test statistic is:
In which X is the sample mean, is the value tested at the null hypothesis,
is the standard deviation and n is the size of the sample.
H0: p = 0.50
This means that:
In a random sample of 305 UGA female students, 128 responded that, if they had a cell phone, they would be willing to walk somewhere after dark that they would normally not go.
This means that
a) Value of the test statistic:
Pvalue:
We are testing the hypothesis that the proportion is less than 0.5, which means that the pvalue of the test is the pvalue of z = -2.81.
Looking at the z-table, z = -2.8 has a pvalue of 0.0026
(b) What is the correct conclusion for this hypothesis test at the 0.05 level of significance?
0.0026 < 0.05, which means that we reject the null hypothesis, that the proportion is 0.5, and accept the alternate hypothesis, that the proportion is less than 0.5, option (1).