Algebra. 8) What is the absolute value of 2 and of -2? Explain.
9) Solve the equation for x: (3x + y)/z = 2
10) ... 8)  Absolute value is the distance from zero on a number line (and has no reference to which direction left/right from zero), so this means the value is always positive:

abs(2) = 2
abs(-2) = 2

9) Solve the equation for x

(3x + y)/z = 2

*multiply both sides by z

(3x + y) = 2z

*subtract y from both sides

3x = 2z - y

*divide both sides by 3

x = (2z - y)/3

10) Which point is a solution to the equation 6x - 5y = 4? Justify your choice
A.   (1, 2)
B.   (1,2)
C.   (-1,2)
D.   (-1, 2)

*plug (x, y) coordinates into equation and see if the result is a valid equation:

6(1) - 5(2) = 4
6 - 10 = 4
-4 = 4            [NO GOOD]

*now try B.   (1,2):

6(1) - 5(-2) = 4
6 - (-10) = 4
6 + 10 = 4
16 = 4            [NO GOOD]

*now try C.   (-1,2):

6(-1) - 5(-2) = 4
-6 - (-10) = 4
-6 + 10 = 4
4 = 4            [OK]

*just for fun let’s also verify D.   (-1, 2) is not the solution, since we found that C. was:

6(-1) - 5(2) = 4
-6 - 10 = 4
-16 = 4           [NO GOOD]

The answer is C.   (-1,2) (and the justification is that we solved for it to be true)

11)  Domain is all values ’x’ (i. e. input)
Range is all values ’y’ (i. e. output)

a. ) y = 2x + 1 is a line with a slope of 2:1 (vert: horiz) and a y-intercept of y = 1, but because it is a line, it extends from -infinty to +infinity for both ’x’ and ’y’, so.

Domain = (-infinity ≤ x ≤ +infinity)
Range = (-infinity ≤ y ≤ +infinity)

b. )  This table on shows discrete values of input/output, so the domain/range is also discrete.

Domain = (3, 7, 11)
Range = (-1,3,5)

c. ) Just from visual confirmation of the plot’s extents.

Domain = (-5 ≤ x ≤ 5)
Range = (-1 ≤ y ≤ 1)

d. ) Again using visual confirmation of the plot’s extents.

Domain = (-2 ≤ x ≤ 2) *note extents are limited by vertical asymptote
Range = (-infinity ≤ y ≤ +infinity)

12)  There are 2 lines of symmetry (they are the vertical line drawn at x = 0, and the horizontal line drawn at y = 0 that bisect the ellipse)

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