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2 years ago

The graph of F(x) can be compressed vertically and shifted to the left to

Mathematics

1 answer:

ryzh [129]2 years ago

5 0

Answer:

G(x) = 1/3 (x + 2)³ ⇒ answer D

Step-by-step explanation:

* Lets explain how to solve the problem

- If the function f(x) translated horizontally to the left by h units, then

the new function g(x) = f(x + h)

- If the function f(x) compressed vertically, then g(x) = k · f(x), where

0 < k < 1 (multiplying each of its y-coordinates by k)

* Lets solve the problem

∵ F(x) = x³

∵ F(x) is compressed vertically

∴ F(x) multiplied by a fraction between 0 and 1

∴ G(x) = k (x³)

∵ F(x) is shifted horizontally to the left

∴ The x add by the shifted units

∴ G(x) = k (x + h)³

* Lets look to the answer to find G(x)

∵ G(x) = 1/3 (x + 2)³

∴ K = 1/3 ⇒ 0 < 1/3 < 1

∴ h = 2 ⇒ + for left shifted

∴ G(x) = 1/3 (x + 2)³

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The, you solve to get the value of the variable.

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2 years ago

Read 2 more answers

What is the volume of the prism?

mezya [45]

Answer:

40 $\frac{5}{8}$ $cm^{3}$

Step-by-step explanation:

The figure is a rectangular prism, so the formula would be Volume = length x width x height.

length = 6 $\frac{1}{2}$ cm

width = 2 $\frac{1}{2}$ cm

height = 2 $\frac{1}{2}$ cm

If you plug everything you have in the problem into the volume equation, you would get : Volume = 6 $\frac{1}{2}$ cm x 2 $\frac{1}{2}$ cm x 2 $\frac{1}{2}$ cm.

Without a calculator, I would first turn the mixed numbers into improper fractions.

6 $\frac{1}{2}$ = $\frac{13}{2}$

2 $\frac{1}{2}$ = $\frac{5}{2}$

Volume = $\frac{13}{2}$ x $\frac{5}{2}$ x $\frac{5}{2}$

When you multiply everything together you should get $\frac{325}{8}$ .

As a mixed number, that would be 40 $\frac{5}{8}$ $cm^{3}$ .

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