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1 year ago

The graph shows the function f(x).

Mathematics

1 answer:

Lerok [7]1 year ago

6 0

The equation that represents the given data is $\RM \\f(x) = -\sqrt[3]{-x} ,$ Option D is the correct answer.

<h3>What is a Function ?</h3>

It is a statement where two variables , one dependent and one independent are related.

It is given that

a cube root function goes through (8, 2), has an inflection point at (0, negative 1), and goes through (8, negative 3).

The equation given in the options are

$\rm f(x) = -\sqrt[3]{x} \\f(x) = -\sqrt[3]{x-1} \\f(x ) =-\sqrt[3]{-x} -1 \\f(x) = -\sqrt[3]{-x}$

The function goes through (8,2)

Substituting the values

f(x) = -2

f(x) = $\sqrt[3]{7}$

f(x) = -3

f(x) = 2

The equation that represents the given data is

$\RM \\f(x) = -\sqrt[3]{-x} ,$ Option D is the correct answer.

To know more about Function

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Nookie1986 [14]

Answer:

$\large\boxed{y=\dfrac{1}{4}x^2-x-4}$

Step-by-step explanation:

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(h, k) - vertex

The focus is

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k = -5

$-5+\dfrac{1}{4a}=-4$ add 5 to both sides

$\dfrac{1}{4a}=1$ multiply both sides by 4

$4\!\!\!\!\diagup^1\cdot\dfrac{1}{4\!\!\!\!\diagup_1a}=4$

$\dfrac{1}{a}=4\to a=\dfrac{1}{4}$

Substitute

$a=\dfrac{1}{4},\ h=2,\ k=-5$

to the vertex form of an equation of a parabola:

$y=\dfrac{1}{4}(x-2)^2-5$

The standard form:

$y=ax^2+bx+c$

Convert using

$(a-b)^2=a^2-2ab+b^2$

$y=\dfrac{1}{4}(x^2-2(x)(2)+2^2)-5\\\\y=\dfrac{1}{4}(x^2-4x+4)-5$

use the distributive property: a(b+c)=ab+ac

$y=\left(\dfrac{1}{4}\right)(x^2)+\left(\dfrac{1}{4}\right)(-4x)+\left(\dfrac{1}{4}\right)(4)-5\\\\y=\dfrac{1}{4}x^2-x+1-5\\\\y=\dfrac{1}{4}x^2-x-4$

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Answer:

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Step-by-step explanation:

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So the answer is 6.7

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