In general, √(y²) = |y|, since y can be positive or negative and y² would have the same value either way.
So,
1) if y > 0, then |y| = y, and
-15√(y²) = -15 |y| = -15y
2) if y < 0, then |y| = -y, and
-√(16y²) = -|4y| = -|4| |y| = -4 (-y) = 4y
Analysis:
1) The graph of function f(x) = √x is on the first quadrant, because the domain is x ≥ 0 and the range is y ≥ 0
2) The first transformation, i.e. the reflection of f(x) over the x axis, leaves the function on the fourth quadrant, because the new image is y = - √x.
3) The second transformation, i.e. the reflection of y = - √x over the y-axis, leaves the function on the third quadrant, because the final image is - √(-x). This is, g(x) = - √(-x).
From that you have, for g(x):
* Domain: negative x-axis ( -x ≥ 0 => x ≤ 0)
* Range: negative y-axis ( - √(-x) ≤ 0 or y ≤ 0).
Answers:
Now let's examine the statements:
<span>A)The functions have the same range:FALSE the range changed from y ≥ 0 to y ≤ 0
B)The functions have the same domains. FALSE the doman changed from x ≥ 0 to x ≤ 0
C)The only value that is in the domains of both functions is 0. TRUE: the intersection of x ≥ 0 with x ≤ 0 is 0.
D)There are no values that are in the ranges of both functions. FALSE: 0 is in the ranges of both functions.
E)The domain of g(x) is all values greater than or equal to 0. FALSE: it was proved that the domain of g(x) is all values less than or equal to 0.
F)The range of g(x) is all values less than or equal to 0.
TRUE: it was proved above.</span>
Answer:
x = -1/2
Step-by-step explanation:
multiply the -4 to all in parentheses
-4(3-2x) +2x =2x -8
-12+8x +2x =2x-8
isolate x by moving whole numbers to other side of equal sign and x to the other side
8x +2x -2x = -8+12
8x = -4
/8
divide by 8 to isolate x
x= -4/8
simplify
x= -1/2
