Answer:
See below.
Step-by-step explanation:
Party A
y = x^2 + 1
For each value of x in the table, substitute x in the equation with that value and evaluate y.
x = -2: y = (-2)^2 + 1 = 4 + 1 = 5
x = -1: y = (-1)^2 + 1 = 1 + 1 = 2
Do the same for x = 0, x = 1, x = 2
x y
-2 5
-1 2
0 1
1 2
2 5
Part B
Look at points (-2, 5) and (-1, 2). The change in x from (-2, 5) to (-1, 2) is 1. The change in y is -3.
Now let's look at two other points which have a change in x of 1. Look at points (0, 1) and (1, 2). The change in x from (0, 1) to (1, 2) is 1. The change in y is 1.
You can see that for the first two points, a change of 1 in x produces a change of -3 in y, but for the second two points, the same change of 1 in x produce a change of 1 in y. Since the same change of x does not always produce the same change in y, the function is nonlinear.
Answer: A
Answer:
reflection
transition left / right are the location of the vertex
Answer:
Increasing a number by 5% and then by 20% is the same as increasing the original number by 26%.
Step-by-step explanation:
Take a number, x.
Now increase it by 5%.
1.05x
Now increase it by 20%.
1.2 * 1.05x = 1.26x
1.26x = 126% of x = 100% of x + 26% of x
100% of x is the same as x, so it is the same as the original x.
The increase is 26% of the original number.
Increasing a number by 5% and then by 20% is the same as increasing the original number by 26%.
All three series converge, so the answer is D.
The common ratios for each sequence are (I) -1/9, (II) -1/10, and (III) -1/3.
Consider a geometric sequence with the first term <em>a</em> and common ratio |<em>r</em>| < 1. Then the <em>n</em>-th partial sum (the sum of the first <em>n</em> terms) of the sequence is

Multiply both sides by <em>r</em> :

Subtract the latter sum from the first, which eliminates all but the first and last terms:

Solve for
:

Then as gets arbitrarily large, the term
will converge to 0, leaving us with

So the given series converge to
(I) -243/(1 + 1/9) = -2187/10
(II) -1.1/(1 + 1/10) = -1
(III) 27/(1 + 1/3) = 18
To qualify as a polynomial, the expression in question:
* Consists of one or more terms * Variables are only with positive whole exponents* No variables in the denominator of any term (the coefficients however, can be fractions.)In that case the answer is most likely: