**Answer:**

**Step-by-step explanation:**

I'm sure you want your functions to appear as perfectly formed as possible so that others can help you. f(x) = 4(2)x should be written with the " ^ " sign to denote exponentation: f(x) = 4(2)^x

f(b) - f(a)

The formula for "average rate of change" is a.r.c. = --------------

b - a

change in function value

This is equivalent to ---------------------------------------

change in x value

For Section A: x changes from 1 to 2 and the function changes from 4(2)^1 to 4(2)^2: 8 to 16. Thus, "change in function value" is 8 for a 1-unit change in x from 1 to 2. Thus, in this Section, the a.r.c. is:

8

------ = 8 units (Section A)

1

Section B: x changes from 3 to 4, a net change of 1 unit: f(x) changes from

4(2)^3 to 4(2)^4, or 32 to 256, a net change of 224 units. Thus, the a.r.c. is

224 units

----------------- = 224 units (Section B)

1 unit

The a.r.c for Section B is 28 times greater than the a.r.c. for Section A.

This change in outcome is so great because the function f(x) is an exponential function; as x increases in unit steps, the function increases much faster (we say "exponentially").

The answer is 88 5/6 . If you were stuck try turning the fractions into improper fractions and multiply both of them and later divide the numerator by the denominator to have a mixed number. You can later simplify the fraction to get 88 5/6. If you need help don't be afraid to tell me in the comments! Hope this helps :)

**Answer:**

Answer in file:

**Step-by-step explanation:**

Step 1: Make sure that the trinomial is written in the correct order; the trinomial must be written in descending order from highest power to lowest power.

Step 2 : Decide if the three terms have anything in common, called the greatest common factor or GCF. If so, factor out the GCF. Do not forget to include the GCF as part of your final answer.

Step 3 : Multiply the leading coefficient and the constant, that is multiply the first and last numbers together.

Step 4 : List all of the factors from Step 3 and decide which combination of numbers will combine to get the number next to x.

Step 5 : After choosing the correct pair of numbers, you must give each number a sign so that when they are combined they will equal the number next to x and also multiply to equal the number found in Step 3.

Step 6 : Rewrite the original problem with four terms by splitting the middle term into the two numbers chosen in step 5.

Step 7 : Now that the problem is written with four terms, you can factor by grouping.

**Answer:**

<em>See above photograph</em>

**Step-by-step ****explanation****:**

This is how your graph will look like with an x-intercept of [−5, 0] (will not see, according to the scale, but on my device, you can), and a y-intercept of [0, 50]. The way to figure out all the coordinates upon this scale is to simply create a y-x value chart. Plug in each input value [x-value] to get your output value [y-value]:

<u>x|y</u>

0|50

1|60

2|70

3|80

4|90

5|100

6|110

7|120

8|130

9|140

10|150

11|160

Then, you simply just draw your line based of this chart.

I am joyous to assist you anytime.