More Algebra 2 problems.

__June 2017, Part I__

All Questions in Part I are worth 2 credits. No work need be shown. No partial credit.

*19. To solve,
*

*Ren multiplied both sides by the least common denominator. Which statement is true?*

(1) 2 is an extraneous solution

(2) 7/2 is an extraneous solution

(3) 0 and 2 are extraneous solutions

(4) This equation does not contain any extraneous solutions.

(1) 2 is an extraneous solution

(2) 7/2 is an extraneous solution

(3) 0 and 2 are extraneous solutions

(4) This equation does not contain any extraneous solutions.

**Answer: (1) 2 is an extraneous solution.**

The equation is undefined for 0 and 2 because of the terms in the denominator. When both sides are multiplied by x^{2} - 2x, that restriction is lifted. If either 0 or 2 are solutions to the equation, then they are extraneous.

Look at the steps below:

At this point, you can check both 0 and 2 to see if they are solutions to the equation.

2(0)^{2} - 11(0 - 2) = 0 - 11(-2) = 22, which is not equal to 8. Zero is not an extraneous solution.

2(2)^{2} - 11(2 - 2) = 2(4) - 11(0) = 8 - 0 = 8. Two *is* an extraneous solution.

As for 7/2, if you finish working out the problem, you will see that it is a solution to the equation, but it is not an extraneous solution.

*20. Given f(9) = -2, which function can be used to generate the sequence -8, -7.25, -6.5, -5.75,...?
(1) f(n) = -8 + 0.75n
(2) f(n) = -8 - 0.75(n - 1)
(3) f(n) = -8.75 + 0.75n
(4) f(n) = -0.75 = 8(n - 1)
*

**Answer: (3) f(n) = -8.75 + 0.75n**

The rate of change is +0.75, which eliminates (2) and (4).

Choice (1) is incorrect because it has an incorrect starting value. If you substitute n = 1, you get -7.25 instead of 8.

Choice (2) would have been correct if there had been addition instead of subtraction.

Choice (3) is the correct answer because adding 0.75 to -8.75 gives you the initial term of -8.

*21. The function
*

*represents a damped sound wave function. What is the average rate of change for this function on the interval [-7,7], to the nearest hundredth?*

(1) -3.66

(2) -0.30

(3) -0.26

(4) 3.36

(1) -3.66

(2) -0.30

(3) -0.26

(4) 3.36

**Answer: (3) -0.26**

To find the average rate of change, calculate f(7) - f(-7) and divide it by (7 - -7). (Like the slope formula.)

This gives you the following equation:

When you plug this into a calculator -- use a lot of parentheses if you have an older operating system! -- you will get -0.261492..., which is -0.26 to the nearest hundredth.

Comments and questions welcome.

More Algebra 2 problems.