The graph of the function f(x) is shown. Which graph represents the function f(2x)

Mathematics

1 answer:

slava [35]3 years ago

8 0

Answer:

It should be the top left graph where there is point (1,1) and (-1, -1) y = 1/x

Step-by-step explanation:

from the original graph, I see:

f(x) = 2/x because f(2) = 1 = 2/2

f(1/4)= 2/(1/4) = 2

...

so then f(2x) compresses f(x) horizontally by a factor of 2

so f(2x) = 2/(2x) = 1/x

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HELP PLEASE i dont understand at all...

bija089 [108]

An exponent signifies repeated multiplication.

$x\cdot x\cdot x=x^{3}$ the factor x is repeated 3 times

Exponents can be added and subtracted to express the effects of multiplication and division.

$\dfrac{x\cdot x\cdot x\cdot x\cdot x}{x\cdot x\cdot x}=\dfrac{x^{5}}{x^{3}}\\\\=\dfrac{x\cdot x\cdot x}{x\cdot x\cdot x}\cdot x\cdot x=x\cdot x\\\\=x^{(5-3)}=x^{2}$

The addition and subtraction of exponents works the same even when there are more denominator factors than numerator factors.

$\dfrac{x\cdot x\cdot x}{x\cdot x\cdot x\cdot x\cdot x}=\dfrac{x^{3}}{x^{5}}=\dfrac{1}{x^{2}}\\\\=x^{(3-5)}=x^{-2}$

That is, a negative numerator exponent is the same as a positive denominator exponent and vice versa. You can move a factor with an exponent from denominator to numerator and change the sign of the exponent, and vice versa.

Your expression has 3 in the denominator with a negative exponent. It can be moved to the numerator and the exponent changed to positive:

$\dfrac{1}{3^{-2}}=3^{2}\\\\=3\cdot 3=\bf{9}$