Question:
The function f(x) is defined as follows:
f(x)= 3x+1 if x is less than or equal to 0
2x^2 if 0 4 if c is greater than or equal to 2
determine the following values of the function
f(-3)= __
f(2)= ___
Answer:
The values are
and ![$f(2)=8$](https://tex.z-dn.net/?f=%24f%282%29%3D8%24)
Explanation:
The function is defined by two parts,
if ![x\leq 0](https://tex.z-dn.net/?f=x%5Cleq%200)
if ![$x \geq 2$](https://tex.z-dn.net/?f=%24x%20%5Cgeq%202%24)
To determine the value of
, we shall substitute the value
in the function
because ![$-3 \leq 0$](https://tex.z-dn.net/?f=%24-3%20%5Cleq%200%24)
Hence, we have,
![f(x) \ \ =3 x+1\\f(-3)=3(-3)+1\\f(-3)=-9+1\\f(-3)=-8](https://tex.z-dn.net/?f=f%28x%29%20%5C%20%5C%20%3D3%20x%2B1%5C%5Cf%28-3%29%3D3%28-3%29%2B1%5C%5Cf%28-3%29%3D-9%2B1%5C%5Cf%28-3%29%3D-8)
Now, to determine the value of
, we shall substitute the value
in the function
because ![$x \geq 2$](https://tex.z-dn.net/?f=%24x%20%5Cgeq%202%24)
Hence, we have,
![f(x)=2 x^{2}\\f(2)=2\left(2^{2}\right)\\f(2)=2(4)\\f(2)=8](https://tex.z-dn.net/?f=f%28x%29%3D2%20x%5E%7B2%7D%5C%5Cf%282%29%3D2%5Cleft%282%5E%7B2%7D%5Cright%29%5C%5Cf%282%29%3D2%284%29%5C%5Cf%282%29%3D8)
Thus, the values are
and ![$f(2)=8$](https://tex.z-dn.net/?f=%24f%282%29%3D8%24)
Answer:
7690.6 cubic feet
Step-by-step explanation:
V=πr^2h
= π x 12^2 x 17
= 7690.6 cubic feet
Answer:
5: given y=2x-2 new y=2x+2
6: given y=-1/4x+4 new y=-1/4x+7
Step-by-step explanation:
Answer:
68% of the distribution will be within one standard deviation of the mean
Step-by-step explanation:
The Empirical Rule states that, for a normally distributed random variable:
68% of the measures are within 1 standard deviation of the mean.
95% of the measures are within 2 standard deviation of the mean.
99.7% of the measures are within 3 standard deviations of the mean.
Bell-shaped = Normally distributed.
This means that 68% of the distribution will be within one standard deviation of the mean
Answer:
Last option (the drawn)
Step-by-step explanation:
The following points correspond to f:
(3, -2), (9, 2)
The slope of the line (m) is:
m = (2 - (-2))/(9 - 3) = 4/6 = 2/3
Therefore, the first option is incorrect (its slope is 3/2).
To find the y-intercept (b) of the line, we replace a known point and the slope into the general equation:
y = mx + b
2 = 2/3(9) + b
b = 2 - 6
b = -4
Therefore, the third option is incorrect (it add 4 instead of subtracting 4).
Replacing x = 6 into the equation we get:
y = 2/3(6) - 4
y = 0
then, point (6, 0) belongs to the line. Therefore, the second option is incorrect (it has the point (6, 1) instead); and the fourth option is correct (it is a line that includes points (0, -4) and (6, 0)).