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Calculus Examples
Popular Problems Calculus Find the Domain and Range f(x)=5x-3
f
(
x
)
=
5
x
−
3
The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.
Interval Notation:
(
−
∞
,
∞
)
Set-Builder Notation:
{
x
|
x
∈
R
}
The range is the set of all valid
y
values. Use the graph to find the range.
Interval Notation:
(
−
∞
,
∞
)
Set-Builder Notation:
{
y
|
y
∈
R
}
Determine the domain and range.
Domain:
(
−
∞
,
∞
)
,
{
x
|
x
∈
R
}
Range:
(
−
∞
,
∞
)
,
{
y
|
y
∈
R
}
The domain- Is the function provides an "output" or value for each member of the domain
Range- The difference between the lowest and highest values.
Answer: x^2 + 9x + 20
Step-by-step explanation:
Foil Method: (a + b) (c + d) = ac + ad + bc + bd
Lets say:
a = x
b = 5
c = x
d = 4
Plugging in the numbers: xx + 4x + 5x + 5*4
Combine like terms:
xx = x^2
4x + 5x = 9x
5 * 4 = 20
You're then left with: x^2 + 9x + 20
Answer:
two numbers are 29 and 17
Step-by-step explanation:
let the number be x
12+x+x=46
2x=46-12
x=34/2
x=17
another number is 12+x
12+17
29
Since the direction is not specified, it can be safe to assume that the direction of rotation is counterclockwise.
300 degrees is 60 degrees less than 360 degrees, which is a full rotation. Thus, 300 degrees counterclockwise is the same as 60 degrees clockwise.
Note that this shape is a hexagon. Thus, we can divide a hexagon into 6 equilateral triangles, each with measures of 60 degrees. Just move OQ to the adjacent clockwise equilateral triangle and see what it overlaps with.
OQ is the altitude of the equilateral triangle, so our answer will be the altitude of the adjacent clockwise equilateral triangle.
The answer is OF.