If a line has a positive slope what is its general direction

1 answer:

6 0

In discussing graphs, we generally agree to move from left to right. If a line has a positive slope, then the function (and the line that represents it) is rising as we move from left to right, as in / .

Exam;ple: y=x is a straight line with the positive slope 1. As x increases, y increases by the same amount.

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Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).

GrogVix [38]

Answer:

D. f^-1(x) = log2(x -6)
4x^2 -3 . . . . x ≤ 0
B. √(x^5) -3√(x^3) -18√x

Step-by-step explanation:

1. When you replace f(x) by x and x by y, you have

... x = 2^y + 6

The first thing you do is subtract 6; then you take the base-2 logarithm:

... (x -6) = 2^y

... log2(x -6) = y = f^-1(x)

You know that to get the y-term by itself, you must subtract 6. Anything else you do will operate on (x-6). Only answer choice D has that sort of construction.

2. When you swap x and y and solve for y, you have ...

... x = -1/2√(y+3)

... -2x = √(y +3) . . . . . . multiply by -2

... (-2x)^2 = y +3 . . . . . square

... 4x^2 - 3 = y = f^-1(x) . . . . subtract 3

The range of f(x) is (-∞, 0], so that is the domain of f^-1(x). That is, f^-1(x) is defined for x ≤ 0.

3. The product of the two functions is ...

... (x -6)(√x)(x +3) = (√x)(x^2 -3x -18)

Every term will have a factor of √x, and the coefficients will be 1, -3, -18. Only selection B matches those conditions.

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