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Algebra Examples
Popular Problems Algebra Find the Domain and Range y=3/2x^2+4x-9
y
=
3
2
x
2
+
4
x
−
9
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:
[
−
35
3
,
∞
)
Set-Builder Notation:
{
y
∣
∣
∣
y
≥
−
35
3
}
Determine the domain and range.
Domain:
(
−
∞
,
∞
)
,
{
x
|
x
∈
R
}
Range:
[
−
35
3
,
∞
)
,
{
y
∣
∣
∣
y
≥
−
35
3
}
image of graph
Answer: There are 12 white and blue cars more than silver and red cars
Number of white cars: n1=25
Number of blue cars: n2=17
Number of white and blue cars: n3=n1+n2=25+17→n3=42
Number of silver cars: n4=21
Number of red cars: n5=9
Number of silver and red cars: n6=n4+n5=21+9→n6=30
How many more white and blue cars are there than silver and red cars?
n=?
n=n3-n6=42-30→n=12
Answer: There are 12 white and blue cars more than silver and red cars.
Answer:
The domain and range remain the same.
Step-by-step explanation:
Hi there!
First, we must determine what increasing <em>a</em> by 2 really does to the exponential function.
In f(x)=ab^x, <em>a</em> represents the initial value (y-intercept) of the function while <em>b</em> represents the common ratio for each consecutive value of f(x).
Increasing <em>a</em> by 2 means moving the y-intercept of the function up by 2. If the original function contained the point (0,x), the new function would contain the point (0,x+2).
The domain remains the same; it is still the set of all real x-values. This is true for any exponential function, regardless of any transformations.
The range remains the same as well; for the original function, it would have been 
. Because increasing <em>a</em> by 2 does not move the entire function up or down, the range remains the same.
I hope this helps!
a number can be written a "x".
"minus" is a key word for subtraction.
"is" is a key word for =.
So if we put that all together, we have
x-3=5
To solve it, we have to add 3, to cancel it out, and add 3 to 5.
x-3=5
+3 +3
x=8
---
hope it helps
