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3 years ago

The function g(x) is graphed.

Mathematics

1 answer:

sergejj [24]3 years ago

3 0

g(1)=-1 : We need to check values of function for x=1. From the graph, we can see, for x=1 the value of y is 1.

So, g(1)=-1 is false.

g(0)=0 : We need to check values of function for x=0. From the graph, we can see, for x=0 the value of y is 0.

So, g(0) =0 is true.

g(4)=-2 :We need to check values of function for x=4. From the graph, we can see, for x=4 the value of y is going up but it's not equal to -2.

So, g(4)=-2 is false.

g(1)=1 :We need to check values of function for x=1. From the graph, we can see, for x=1 the value of y is 1.

So, g(1) =1 is true.

g(-1)=1 :We need to check values of function for x=-1. From the graph, we can see, for x=-1 the value of y is 1.

So, g(-1)=1 is true.

g(4)=2 :We need to check values of function for x=4. From the graph, we can see, for x=4 the value of y is going up but it's not equal to 2.

So, g(4)=2 is false.

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2 years ago

Read 2 more answers

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Mamont248 [21]

Answer:

1)The rocket hit the ground at $x = \frac{5}{4}$

2)The maximum height of the rocket = 12.468 feet

Step-by-step explanation:

Step(i):-

Given equation

y = -2 x² + 5 x + 7 ...(i)

Differentiating equation (i) with respective to 'x' , we get

$\frac{dy}{dx} = -2( 2x) +5(1) = -4x +5$

Equating zero

$\frac{dy}{dx} = 0$

⇒ -4 x +5 =0

⇒ -4 x = -5

⇒ $x = \frac{5}{4}$

The rocket hit the ground at $x = \frac{5}{4}$

Step(ii):-

$\frac{dy}{dx} = -4x +5$ ...(ii)

Again differentiating equation (ii) with respective to 'x' , we get

$\frac{d^{2} y}{dx^{2} } = - 4(1)$

The maximum height at x = $\frac{-5}{4}$

y = -2 x² + 5 x + 7

$y = -2 (\frac{5}{4})^{2} + 5 (\frac{5}{4} ) + 7$

$y = \frac{-2(25)+ 25 (16)+7(64)}{64}$

$y = \frac{798}{64} = 12.468 feet$

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