Write an equation that represents a horizontal translation 10 units left of the graph of g(x) = |x|

Mathematics

2 answers:

Vika [28.1K]3 years ago

7 0

Answer: h(x) = |x+10|

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Explanation:

To shift the graph 10 units to the left, we replace x with x+10. What's really going on is that the xy axis shifts 10 units to the right (because x is now x+10; eg, x = 2 ---> x+10 = 2+10 = 12) so it appears that the graph is moving to the left. The general rule is h(x) = g(x+10).

So,
g(x) = |x|
g(x+10) = |x+10| ... every x has been replaced with x+10
h(x) = g(x+10)
h(x) = |x+10|

We can use a graphing tool like GeoGebra to visually confirm we have the right answer (see attached). Note how a point like (0,0) on the green graph moves to (-10,0) on the red graph.

prisoha [69]3 years ago

4 0

To move a graph c units to the right, minus c from every x
to move a graph c units to the left, add c to every x

g(x)=|x|
move to left 10 units
add 10 to every x
h(x)=|x+10| is the equation of g(x) translated 10 units to the left

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And we can use the z score formula given by:

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And using the z score we have:

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And we can use the normal standard distribution table or excel in order to find the probabilities and we got:

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Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Solution to the problem

Let X the random variable that represent the time it takes her to complete one review, and for this case we know the distribution for X is given by:

$X \sim N(4,1.2)$

Where $\mu=4$ and $\sigma=1.2$

And we select a sample size of n =16. Since the dsitribution for X is normal then the distribution for the sample mean $\bar X$ is also normal and given by: