Grade 9 transformation graph

1) D

2) C

3) A

4) B

Step-by-step explanation:

Ok, we need to try each function in the point x = 0 and then analyze the limit as x goes to really large values.

1) g(x) = -3^x

When x = 0, we have:

g(0) = -3^0 = -1

Then we know that the graph of this function will be either A or D.

Now, as x goes to really large values, 3^x will eventually approximate to infinity.

Then - 3^x will approximate to negative infinnity.

From that, we can conclude that the graph for this function is the one that goes to negative infinite as x increases. That is graph D.

2) h(x) = (1/3)^(-x) = 3^x

This is the exact opposite of the previous function. So we need to find the graph that is an exact reflection across the x-axis of graph D, and that one is the graph C.

then the graph if this function is C.

3) k(x) = - (1/3)^x = -1/(3^x)

When x = 0

k(0) = -(1/3)^0 = -1

We have two options with a y-intersect at y = -1  (graph A and D) and in this case, we can see that the part that grows fast is in the denominator, then as x increases, the denominator increases, and thus the function will tend to zero, then the graph of this function is graph A.

4) g(x) =  3^(-x) = 1/(3^x)

g(0) = 1/(3^0) = 1/1 = 1

And same as before, as x increases, g(x) tends to zero.

Then the remaining graph (B) is the graph of this function.

step-by-step explanation:

i found the life tables for the year 2012. 

life table of males at age 30. probability of dying between ages x and x+1

total population:  

29–30 . . . . . . . . . . . . 0.001030

30–31 . . . . . . . . . . . . 0.001061

males:  

29–30 . . . . . . . . . . . . 0.001420

30–31 . . . . . . . . . . . . 0.001448

white population

29–30 . . . . . . . . . . . . 0.001005

30–31 . . . . . . . . . . . . 0.001037

white males

29–30 . . . . . . . . . . . . 0.001372

30–31 . . . . . . . . . . . . 0.001399

non hispanic white population

29–30 . . . . . . . . . . . . 0.001083

30–31 . . . . . . . . . . . . 0.001116

non hispanic white males

29–30 . . . . . . . . . . . . 0.001477

30–31 . . . . . . . . . . . . 0.001503

jacob, non hispanic white male. 30 years old.

probability that jacob lives to be 30 years old. 

since the given probabilities are probabilities of dying, i think we simply subtract it from 1 to get the probability of living. we will use the probability of non hispanic white male.

                                          probability of living to be 30 y.o.

29 - 30 : 1 - 0.001477 = 0.998523

30 - 31 : 1 - 0.001503 = 0.998497

explanation:

remove parenthesis:

=

apply rule

=

multiply fractions:

=

=

divide:

=

mordancy.