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Vilka [71]
3 years ago
7

The function f(x) is represented by the table below. What are the corresponding values of g(x) for the transformation g(x)=2f(x)

Mathematics
1 answer:
malfutka [58]3 years ago
3 0

Answer:

see the explanation

Step-by-step explanation:

we know that

g(x)=2f(x)

so

Find the value of g(x) for the corresponding value of f(x)

1) For x=-6, f(x)=2

Substitute

g(x)=2f(x)

g(x)=2(2)=4

2) For x=-2, f(x)=2

Substitute

g(x)=2f(x)

g(x)=2(2)=4

3) For x=0, f(x)=6

Substitute

g(x)=2f(x)

g(x)=2(6)=12

4) For x=1, f(x)=3

Substitute

g(x)=2f(x)

g(x)=2(3)=6

4) For x=6, f(x)=-1

Substitute

g(x)=2f(x)

g(x)=2(-1)=-2

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Given that f(–2.4) = -1 and f(-1.9) = -8, approximate<br> f'(-2.4).<br> f'(-2.4)
lora16 [44]

Answer:

f'(-2.4) ≈ -14

General Formulas and Concepts:
<u>Algebra I</u>

Coordinate Planes

  • Coordinates (x, y)

Slope Formula: \displaystyle m = \frac{y_2 - y_1}{x_2 - x_1}

Functions

  • Function Notation

<u>Calculus</u>

Differentiation

  • Derivatives
  • Derivative Notation

Step-by-step explanation:

*Note:

The definition of a derivative is the slope of the <em>tangent</em> <em>line</em>.

<u>Step 1: Define</u>

<em>Identify.</em>

f(-2.4) = -1

f(-1.9) = -8

<u>Step 2: Differentiate</u>

Simply plug in the 2 coordinates into the slope formula to find slope <em>m</em>.

  1. [Derivative] Set up [Slope Formula]:                                                           \displaystyle f'(-2.4) \approx \frac{f(x_2) - f(x_1)}{x_2 - x_1}
  2. Substitute in coordinates:                                                                           \displaystyle f'(-2.4) \approx \frac{-8 - -1}{-1.9 - -2.4}
  3. Evaluate:                                                                                                       \displaystyle f'(-2.4) \approx -14

---

Learn more about derivatives: brainly.com/question/17830594

---

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Differentiation

6 0
2 years ago
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