The linearly functions f(x) and g(x) are represented on the graph , where g(x) is a transformation of f(x) Part A: Describe two types of transformations that can be used to transform f(x) to g(x). (2 points) Part B: Solve for k in each type of transformation. (4 points) Part C: Write an equation for each type of transformation that can be used to transform f(x) to g(x). (4 points)

Step-by-step explanation:

A, C. The two kinds of transformations are

__

B. For the vertical translation, we note that ...

  g(0) = 6

  f(0) = -10

so ...

  g(0) = f(0) +k

  k = g(0) -f(0) = 6 -(-10) = 16

__

For the horizontal translation, we note that ...

  g(-3) = 0 = f(5) = f(-3-k)

  5 = -3 -k

  k = -8 . . . . . add k-5 to both sides

In summary:

d. 24+-0.114

step-by-step explanation:

the question requires us to calculate the approximate 95% confidence interval for the mean number of ounces of ketchup per bottle in the sample given the following statistics;

sample mean = 24

standard deviation, σ = 0.4

sample size , n = 49

the confidence interval for a population mean is calculated using the formula;

sample mean ± z-score*(σ/sqrt(n))

the z-score associated with a 95% confidence interval, from the standard normal tables, is;

1.96

substituting these values into the formula;

24 ± 1.96*(0.4/7)

= 24 ± 0.112

from the alternatives given, choice d is closest to the above expression;