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Alex Ar [27]
3 years ago
15

Could you please help with this question for domain, range, and end behavior? I started it, but I think I'm doing it wrong.

Mathematics
1 answer:
Tanzania [10]3 years ago
8 0

It looks like you have the domain confused for the range! You can think of the domain as the set of all "inputs" for a function (all of the x values which are allowed). In the given function, we have no explicit restrictions on the domain, and no situations like division by 0 or taking the square root of a negative number that would otherwise put limits on it, so our domain would simply be the set of all real numbers, R. Inequality notation doesn't really use ∞, so you could just put an R to represent the set. In set notation, we'd write

\{x\in\re\mathbb{R}\}

and in interval notation,

(-\infty,\infty)

The <em>range</em>, on the other hand, is the set of all possible <em>outputs</em> of a function - here, it's the set of all values f(x) can be. In the case of quadratic equations (equations with an x² term), there will always be some minimum or maximum value limiting the range. Here, we see on the graph that the maximum value for f(x) is 3. The range of the function then includes all values less than or equal to 3. As in inequality, we can say that

f(x)\leq3,

in set notation:

\{f(x)\in\mathbb{R}\ |\ f(x)\leq3\}

(this just means "f(x) is a real number less than or equal to 3")

and in interval notation:

(-\infty,3]

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Solve for the variable. Show each step in the solution process.​
motikmotik

Answer:

z = 1/2

Step-by-step explanation:

Step 1: Write equation

22z + 6 - 10 = 6z + 4

Step 2: Solve for <em>z</em>

  1. Combine like terms: 22z - 4 = 6z + 4
  2. Subtract 6z on both sides: 16z - 4 = 4
  3. Add 4 to both sides: 16z = 8
  4. Divide both sides by 16: z = 8/16
  5. Simplify: z = 1/2

Step 3: Check

<em>Plug in z to verify it's a solution.</em>

22(1/2) + 6 - 10 = 6(1/2) + 4

11 - 4 = 3 + 4

7 = 7

6 0
3 years ago
can someone help me with this? this is algebra 2 question and please show me all work (orderd pair, vertex, graph ect..)
Andrews [41]
To find the maximum height you need to find the vertex:(h,k)  
Your equation is in vertex form a(x-h)+k and the vertex is (h,k) where k is the maximum height and the h is the distance it went to reach the maximum height.
k=6 so the kangaroo's maximum height is 6 feet.

To find how long is the kangaroo's jump, take a look at the graph. You will notice that the parabola ends at the distance the kangaroo jumped. You will also see that it is the one of the x-intercepts. 

 
 -.03(x-14)^2+6=0
-.03(x-14)^2+6-6=0-6
-.03(x-14)^2=-6
-.03/-.03(x-14)=-6/-.03
(x-14)^2=200
[(x-14)^2]^.5=200^.5
x-14=(200)^.5
x-14+14=(200)^.5+14
x≈28.14 feet
The kangaroo jumped a distance of 28.14 feet.

You will notice that the square root of a number gives you two solutions a positive and a negative one. The other solution is -.14, which we know distance is not negative so we do not use that solution. Also, I used the ^.5 instead of using the square root. It is the same. 


8 0
3 years ago
Help me answer this question please
Lynna [10]

Answer:

The hours times 4 equals the miles. The answer is B.

Step-by-step explanation:


7 0
3 years ago
Find the value. please help!
ZanzabumX [31]
A= 2.5
b= 2
LM/ON= 15
LO/MN= 5
8 0
2 years ago
Help pls with math lotsss of points!!!
sveticcg [70]

Answer:

5x^2+22x-12         x cannot be -5, -4, -2

(x+5)(x+4)(x+2)

Step-by-step explanation:

In order to solve this, your denominator must be the same. Let's start by writing out the two different quadratic formulas:

x^2 + 6x + 8 <-- This should factor out to (x+4)(x+2)

x^2 + 7x + 10 <-- This should factor out to (x+5)(x+2)

Now that you have factored out the two quadratics, plug them into the equation.

    5x        -       3

(x+4)(x+2)      (x+5)(x+2)

Now as we know, -2 cannot be x because it will turn the entire equation undefined. Multiple top and bottom with (x+5) on the right side and (x+4) on the left side.

5x (x+5)             -           3(x+4)  

(x+5)(x+4)(x+2)      (x+5)(x+4)(x+2)

Focus on the top. 5x(x+5) will turn out to be 5x^2+25x. 3(x+4) will turn out to be 3x+12. Combine the two equations because now they are equal to each other and do the subtraction:

5x^2+25x - (3x+12)     =    5x^2+22x-12         x cannot be -5, -4, -2

 (x+5)(x+4)(x+2)               (x+5)(x+4)(x+2)

4 0
2 years ago
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