Example 1
Write y = x2 + 4x + 1 using function notation and evaluate the function at x = 3.
Solution
Given, y = x2 + 4x + 1
By applying function notation, we get
f(x) = x2 + 4x + 1
Evaluation:
Substitute x with 3
f (3) = 32 + 4 × 3 + 1 = 9 + 12 + 1 = 22
Example 2
Evaluate the function f(x) = 3(2x+1) when x = 4.
Solution
Plug x = 4 in the function f(x).
f (4) = 3[2(4) + 1]
f (4) = 3[8 + 1]
f (4) = 3 x 9
f (4) = 27
Example 3
Write the function y = 2x2 + 4x – 3 in function notation and find f (2a + 3).
Solution
y = 2x2 + 4x – 3 ⟹ f (x) = 2x2 + 4x – 3
Substitute x with (2a + 3).
f (2a + 3) = 2(2a + 3)2 + 4(2a + 3) – 3
= 2(4a2 + 12a + 9) + 8a + 12 – 3
= 8a2 + 24a + 18 + 8a + 12 – 3
= 8a2 + 32a + 27
Answer:
The standard deviation of the sampling distribution of x overbarx, denoted sigma Subscript x overbarσx, is called the standard error of the mean . The standard deviation of the sampling distribution of x overbarx, denoted sigma Subscript x overbarσx, is called the standard distribution of the sample.
Step-by-step explanation:
The standard error (SE) of a statistic is the standard deviation of its sampling distribution or an estimate of that standard deviation. It is called the standard error of the mean (SEM) if the parameter or the statistic is the mean.
Mark has to ride 50 kilometers. He already rode 18.23 and 13.94.
18.23km+13.94km=32.17km
50km-32.17km=17.83km
Mark will have to ride 17.83km more. The correct answer is B.
With this, we have have a few things going on here. First notice the chain rule needed for 3x and then that d/dx sinx = cosx , d/dx cosx = -sin× , d/dx -sinx = - cos and finally
d/dx -cosx = sinx. In knowing these derivatives, you know that you need to take the derivative FOUR times to return it back to itself. Doing the 77th derivative makes you do taking the derivative in these 4 time "cycles" 19 times (bc 77/4 = 19.25) which leaves you with taking the derivative just ONCE more after the first 76 times. So the 77th derivative of sinx is cosx. That is not all though. Recognixe that you will also multiply it by 3 77times bc of chain rule, so the 77th derivative of sin (3x) is......: ( 3^77 × cos (3x) )
