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1 year ago

If f(x) = x^3 and g(x) = -2x^3, how has f(x) been transformed to get g(x)?

1 answer:

4 0

The transformation that is applied to f(x) to get g(x) is that the function f(x) is vertically stretched by a factor of -2.

<h3>How does the transformation of a function happen?</h3>

The transformation of a function may involve any change.

Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs) etc.

If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:

Horizontal shift (also called phase shift):

Left shift by c units, y=f(x+c) (same output, but c units earlier)
Right shift by c units, y=f(x-c)(same output, but c units late)

Vertical shift

Up by d units: y = f(x) + d
Down by d units: y = f(x) - d

Stretching:

Vertical stretch by a factor k: y = k × f(x)
Horizontal stretch by a factor k: y = f(x/k)

If f(x) = x³ and g(x) = -2x³, then the transformation that is applied to f(x) to get g(x) is that the function f(x) is vertically stretched by a factor of -2.

Hence, the transformation that is applied to f(x) to get g(x) is that the function f(x) is vertically stretched by a factor of -2.

Learn more about Transforming functions:

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Answer:

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

$p_v =P(z$

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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

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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.

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2 years ago