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4 years ago

Is the following function even, odd or neither? f(x)=x^3 +4x

Mathematics

1 answer:

erica [24]4 years ago

6 0

Answer:

D, neither

Step-by-step explanation:

to determine whether a function is even, odd or neither, we need to know what it means

an even function is symmetric with respect to the y-axis

an odd function is symmetric with respect to the origin

to solve an equation to see if its even or odd, we would need to substitute <em>x</em> in the equation for <em>-x</em>.

in an even function when we substitute f(-x), it should be equal to to f(x)

in an odd function when we substitute f(-x), it should be equal to -f(x)

so lets test the function given to see if its even

f(x) = x³ + 4x

f(-x) = (-x)³ + 4(-x)

f(-x) = x³ - 4x

f(-x) = x³ - 4x ≠ f(x) = x³ + 4x

comparing this to the orignal function, we see that f(-x) = x³ - 4x is not even as we did not get the same output as the original function

now we should test to see if its odd. we have already seen what f(-x) is, now lets try -f(x) and compare it to f(-x) and f(x)

-f(x) = -(x³ + 4x) -->

-f(x) = -x³ - 4x ≠ f(-x) = x³ - 4x

f(-x) = x³ - 4x ≠ f(x) = x³ + 4x

comparing this to f(x) and f(-x), we see that it not odd as we did not get the same output

so the answer is D, neither even nor odd

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Answer:

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Step-by-step explanation:

This question has to do with a factor of numbers which we refer to as:

Lowest common multiple.

Lowest common multiple can be defined as the Lowest multiple that is common to the multiple of two numbers.

We are told in the question that:

Lloyd is making goblins and elves on a video game. It takes 6 rounds to make a goblin and 8 rounds to make an elf.

We find the multiples of 6 and 8

6 = 1, 6, 12, 18, 24, 48, 54, 60, 66, 72 e.tc.

8 = 1, 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, e.t.c

The Lowest Common Multiple: This is the least or lowest multiple that is common to both 6 and 8

= 24.

Therefore, it will take 24 rounds for Lloyd to complete another goblin and elf at the same time

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Answer:

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Step-by-step explanation:

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Step-by-step explanation:

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Read 2 more answers

Kids with cell phones: A marketing manager for a cell phone company claims that less than 58% of children aged 8-12 have cell ph

Vikentia [17]

Answer:

$z=\frac{0.54 -0.58}{\sqrt{\frac{0.58(1-0.58)}{820}}}=-2.32$

$p_v =P(z$

Since the p value is lower than the significance level $\alpha=0.1$ we have enough evidence to reject the null hypothesis and the claim for the manager makes sense.

For the Ti84 preocedure we need to do this:

STAT> TESTS> 1-Z prop Test

And then we need to input the following values:

po= 0.58

x = 443 , n= 820

prop <po

And then calculate and we will get the same results

Step-by-step explanation:

Data given and notation

n=820 represent the random sample taken

X=443 represent the people that had cell phones

$\hat p=\frac{443}{820}=0.540$ estimated proportion of people that had cell phones

$p_o=0.58$ is the value that we want to test

$\alpha=0.1$ represent the significance level

Confidence=90% or 0.90

z would represent the statistic (variable of interest)

$p_v$ represent the p value (variable of interest)

System of hypothesis

We need to conduct a hypothesis in order to test the claim that the true proportion is less than 0.58.:

Null hypothesis: $p\geq 0.58$

Alternative hypothesis: $p < 0.58$

The statistic is given by:

$z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}$ (1)

And replacing we got:

Since we have all the info requires we can replace in formula (1) like this:

$z=\frac{0.54 -0.58}{\sqrt{\frac{0.58(1-0.58)}{820}}}=-2.32$

Decision

The significance level provided $\alpha=0.1$ . Now we can calculate the p value

Since is a left tailed test the p value would be:

$p_v =P(z$

Since the p value is lower than the significance level $\alpha=0.1$ we have enough evidence to reject the null hypothesis and the claim for the manager makes sense.

For the Ti84 preocedure we need to do this:

STAT> TESTS> 1-Z prop Test

And then we need to input the following values:

po= 0.58

x = 443 , n= 820

prop <po

And then calculate and we will get the same results

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