What is the affect on the graph of the linear parent function f(x) equals X when FX is replaced by FX +3
1 answer:
Answer:
The graph of the f(x) will horizontal shift left by 3 when f(x) is replaced by f(x+3).
Step-by-step explanation:
We know that when we add a constant to the input of the parent function, we get a horizontal shift.
The direction of shifting depends upon the value of the added constantly. If the added constant is negative, the shift of the graph will be left and if the added constant is positive, the shift of the graph will be right.
For example, consider the function
f(x)
so adding in the put i.e.
would be a change on the inside of the function, giving a horizontal shift left by 3.
Therefore, the graph of the f(x) will horizontal shift left by 3 when f(x) is replaced by f(x+3).
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Answer:
And if we solve for a we got
So the value of height that separates the bottom 10% of data from the top 90% is 64.08.
The graph attached illustrate the situation.
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 heights of a population, and for this case we know the distribution for X is given by:
Where and
For this part we want to find a value a, such that we satisfy this condition:
(a)
(b)
Both conditions are equivalent on this case. We can use the z score again in order to find the value a.
As we can see on the figure attached the z value that satisfy the condition with 0.10 of the area on the left and 0.90 of the area on the right it's z=-1.28. On this case P(Z<1.64)=0.95 and P(z>1.64)=0.05
If we use condition (b) from previous we have this:
But we know which value of z satisfy the previous equation so then we can do this:
And if we solve for a we got
So the value of height that separates the bottom 10% of data from the top 90% is 64.08.
The graph attached illustrate the situation.
