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Sedaia [141]
2 years ago
6

Which two transformations must be applied to the graph of y = ln(x) to result in the graph of y = –ln(x) + 64?

Mathematics
1 answer:
stiks02 [169]2 years ago
3 0

Answer: A) reflection over the x-axis, plus a vertical translation

Step-by-step explanation:

Ok, when we have a function y = f(x)

> A reflection over the x-axis changes a point (x, y) to a point (x, -y), then for a function (x , y = f(x)) the point will change to (x, -y =- f(x))

then for a funtion g(x), this tranformation can be written as h(x) = -g(x).

> A vertical translation of A units (A positive) up for a function g(x) can be written as: h(x) = g(x) + A.

Then in this case we have:

y = g(x) = ln(x)

and the transformed function is h(x) = -ln(x) + 64

Then we can start with h(x) = g(x)

first do a reflection over the x-axis, and now we have:

h(x) = -g(x) = -ln(x)

And now we can do a vertical translation of 64 units up

h(x) = -g(x) + 64 = -ln(x) + 64

Then the correct option is:

A) reflection over the x-axis, plus a vertical translation

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The function y = f (x) is graphed below. What is the average rate of change of the function f(x) on the interval - 1 ≤ x ≤ 3?
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Answer:

\displaystyle -2

General Formulas and Concepts:

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

  1. Brackets
  2. Parenthesis
  3. Exponents
  4. Multiplication
  5. Division
  6. Addition
  7. Subtraction
  • Left to Right

<u>Algebra I</u>

  • Average Rate of Change: \displaystyle \frac{f(b) - f(a)}{b - a}

Step-by-step explanation:

<u>Step 1: Define</u>

Interval -1 ≤ x ≤ 3

a = -1, b = 3

f(a) = f(-1) = 4

f(b) = f(3) = -4

<u>Step 2: Find Average</u>

  1. Substitute in variables [ARC]:                     \displaystyle \frac{f(3) - f(-1)}{3 + 1}
  2. Substitute:                                                   \displaystyle \frac{-4 - 4}{3 + 1}
  3. [Fraction] Subtract/Add:                             \displaystyle \frac{-8}{4}
  4. [Fraction] Divide:                                        \displaystyle -2
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84.95 with 20% tip: 107.34

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125 with 20% tip: 150

12.45 with 15% tip: 14.38

12.45 with 20% tip: 14.94

Step-by-step explanation:

Take value on the vertical column and multiply it by either 1.15 or 1.2

3 0
3 years ago
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