On a coordinate plane, a parabola opens down. It has an x-intercept at (negative 5, 0), a vertex at (negative 1, 16), a y-intercept at (0, 15), and an x-intercept at (3, 0).
The function f(x) = –x2 − 2x + 15 is shown on the graph. What are the domain and range of the function?
The domain is all real numbers. The range is {y|y < 16}.
The domain is all real numbers. The range is {y|y ≤ 16}.
The domain is {x|–5 < x < 3}. The range is {y|y < 16}.
The domain is {x|–5 ≤ x ≤ 3}. The range is {y|y ≤ 16}
Answers
Answer:
Step-by-step explanation:
Domain is all the x's and range is all the y's. There's no reason why you couldn't pop any x into the given equation and calculate it and get a number out. So literally ANY x can be used and found on this graph. So the domain is all real numbers, one of the first two answers is going to be the right one. Now, the range is all the y's on the graph. The problem says that the parabola opens down, which means it has a highest point. There is no graph above that point. That's the point (-1, 16). So 16 is the highest y-value you can find on the graph. All the rest of the y's are smaller. The range is all the y's such that the y's are 16 and smaller...in math that's written {y | y <= 16} So the second answer is the right one.
The domain is all real numbers. The range is {y | y ≤ 16}
How to determine the domain and the range?The attached graph completes the question
Calculating the domain
The function is given as:
f(x) = -x² - 2x - 15
The above function is a parabola or a quadratic function.
Quadratic functions have their domain to be the set of all real numbers.
Hence, the domain is all real numbers.
Calculating the range
On the graph, we have the maximum value of y to be:
Maximum = 16
Because the parabola opens down, the range would be:
y ≤ 16
Hence, the range is {y | y ≤ 16}
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Related Questions
You are selling candy for $2 each and burgers for $5 each. You have a budget for $150. The equation for this situation can be written as 2x+5y=150
Find the x intercept and y intercept. Show all work.
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If you are selling 0 burgers, how many candies did you sell? Show your work.
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Answer:
12 with a remainder of 5
Step-by-step explanation:
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The table shows the thickness of four items. Place the items in order from the greatest thickness to the least thickness.
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Dwayne is selling hamburgers and cheeseburgers. He has 100 burger buns. Each hamburger sells for $3, and each cheeseburger sells for $3. 50. Which system of inequalities represents the number of hamburgers, h, and the number of cheeseburgers, c, he must sell to have sales of at least $80? h c ≤ 80 3h 3. 5c ≤ 100 h c ≤ 80 3h 3. 5c ≥ 100 h c ≤ 100 3h 3. 5c ≤ 80 h c ≤ 100 3h 3. 5c ≥ 80.
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Answer: See below
Step-by-step explanation:
Let h represent hamburgers and c represent cheeseburgers
h + c ≤ 100 - The amount of burgers sold
3h + 3.5c ≥ 80 - Amount that each burger sells for
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A)4
B)2.9
C)3.8
Answers
Answer: C
Step-by-step explanation:
a point moves so that it's y-coordinate is always 2 less than it's x-coordinate.
1) write an equation for it's path
2)where does it cross the x-axis
3) where does it cross the y-axis
4) what is it's slope
Answers
Step-by-step explanation:
y is always 2 less than x
1) y = x- 2
2) where does it cross the x-axis ? that means y = 0.
0 = x - 2
x = 2
3) where does it cross the y-axis ? that means x = 0
y = 0 - 2 = -2
4) the slope is always the factor of x.
in
y = x - 2.
the factor of x is simply +1.
If its y-coordinate is always 2 less than its x-coordinate, this is expressed as y = x - 2
Slope and equationsFrom the given information
Let the y-coordinate be yLet the x-coordinate be xIf its y-coordinate is always 2 less than its x-coordinate, this is expressed as:
y = x - 2
The equation of the path is y - x - 2
2) The point where th line cuts the x-axis is at y = 0
0 = x - 2
x = 2
The point is at (2, 0)
3) The point where th line cuts the y-axis is at x = 0
y = 0 - 2
y = -2
The point is at (0, -2)
4) The standard equation of a line is y = mx + b where m is the slope. Given the equation y = x - 2
Comparing:
mx = 1x
m = 1
Hence the slope of the equation is 1
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Answer:
i dont know
Step-by-step explanation:
I honestly don’t know
Answers
Answer:
x=-3h
x=-12
Step-by-step explanation:
[tex]\frac{x}{h} +1=-2[/tex]
[tex]\frac{x}{h} =-3[/tex]
[tex]x=-3h[/tex]
[tex]x=-3(4)[/tex]
[tex]x=-12[/tex]
Which of the following ordered pairs is the solution to the following system of equations?
X + y = 11
x - 4y = -14
(5,6)
(5-6)
(6,5)
(6,-5)
Answers
To cancel a term from both equations you have to multiple the top one by 4 so
4x + 4y = 44
x - 4y = -14
cancel out the y’s from both equations and add the terms from both so you’ll have
5x = 30
divide by 5
x = 6
substitute 6 for x in the first equation
6+y=11
subtract 6 from both sides
y = 5
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what is the 78th term of the arithmetic sequence -4, -2, 0,
Answers
Answer:
T78=150
Step-by-step explanation:
Tn=a+(n-1)d
T78=-4+(78-1)2
T78 =-4+(77)2
T78 =-4+154
T78=150
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Answer:
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Step-by-step explanation:
she put 4 stickers on each car
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Answers
Answer:
46.85
Step-by-step explanation:
He had $46.85 to begin with, because 27.70 + 19.15 is equal to 46.85
Hannah is making cakes for the bake sale at her school. Each cake requires 1 1/2 cups of sugar. How many complete cakes can Hanna make if she has 6 3/4 cups of sugar?
Help please ? :)
Answers
Answer:
4
Step-by-step explanation:
Divide 6 3/4 by 1 1/2
Convert into improper fractions, 27/4 and 3/2
[tex]\frac{27}{4} / \frac{3}{2}[/tex]
[tex]\frac{27}{4} * \frac{2}{3}[/tex]
[tex]\frac{9}{2} = 4.5[/tex]
The question asks for the number of whole cakes, so the answer would be 4.
Answer : 4
Step - by - step explanation :
In - order to find out how many cakes Hannah can make we need to find out how many 1 1/2 cups of sugar she has . . .
what is 6 3/4 divided by 1 1/2 --> 6 3/4 divided by 1 2/4 ? 4 1/2
SO ! Hannah can make 4 complete cakes
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(B 12 - 10
(C -10 + 12
(D -10 - 12
Answers
Answer: D -10 - 12
Step-by-step explanation:
Temperature change is (Final T) - (Initial T)
(Final T) = -10C
(Initial T) = 12
(Final T) - (Initial T) = -10C - 12C
Temp Change - 22C
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Answers
Answer:
e = 99 , d = 90 , f = 81
Step-by-step explanation:
Answer:
81º
Step-by-step explanation:
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Answer:
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Step-by-step explanation:
a² + b² = c²
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Answer:
22 33/40
Step-by-step explanation:
Answer:
Step-by-step explanation:
1. Classify the following polynomials as monomial, binomial trinomial and polynomial:
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Answer:
binomial
Step-by-step explanation:
a monomial has 1 term
a binomial has 2 terms
a trinomial has 3 terms
2x + y has 2 terms and so is a binomial
Select the point - slope form of the line
Select one:
a.
y − y1 = m ( x − x1 )
b.
ax + by + c = 0
c.
x / a + y / b = 1
d.
y = mx + b
Answers
Answer:
y − y1 = m ( x − x1 )
Step-by-step explanation:
Point slope form would include a slope 'm' and a point (x1, y1).
The first option is the general formula for point-slope form.
B is standard form for a straight line (it can also be Ax + By = C)
C is intercept form.
D is slope-intercept form.
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Put the following equation of a line into slope-intercept form, simplifying all fractions. 3x+6y=-42
Answers
Answer:
y = -1/2x + 7
Step-by-step explanation:
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6y = -3x + 42. You want 1y by itself, so divide everything by 6.
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Answer: 13 units
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Answer:
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Answers
Answer:
65--but the method is the important part that the directions indicated.
Step-by-step explanation:
26 + 39
(2 × 13) + (3 × 13)
The GCF is 13.
Factor the 13 out; it's like Distributive Property in reverse.
13 (2 + 3)
13 (5)
65
26+39= 65, so we obtain the same answer as just adding, by using GCF and Distributive Property.
Answer:
13(2 +3)
Step-by-step explanation:
26 = 2·13
39 = 3·13
The greatest common factor is 13, so the sum can be written ...
26 +39 = 13(2 +3)
_____
Additional comment
Of course, the value of the sum is ...
13(2+3) = 13(5) = 65
Alternatively, the sum can be evaluated as ...
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Answers
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a.7/4x
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Step-by-step explanation:
What is the slope of this line?
Enter your answer as a whole number or a fraction in simplest form in the box.
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Answers
Answer:
1/4
Step-by-step explanation:
We know two points on the line so we can use the slope formula
(0,6) and (8,8)
m = ( y2-y1)/(x2-x1)
= (8-6)/(8-0)
= 2/8
= 1/4
Answer:
1/4
Step-by-step explanation:
slope=rise/run=1/4
1 ton is equal to 2,000 pounds. How many pounds are in 5 tons, 230 pounds?
Answers
Answer: 10230
Step-by-step explanation:
The amount in pound is 1230 pounds.
What is Unitary Method ?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.
For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.
12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.
As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.
This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.
Given:
1 ton is equal to 2,000 pounds.
So, 5 tons and 230 pounds
= 5 x 2000 + 230
= 1000 + 230
= 1230 pounds.
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