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Alexus [3.1K]
3 years ago
8

The graph of the function f(x)=-(x+3)(x-1) is shown below.Which is true about the domain and range of the function

Mathematics
2 answers:
Vika [28.1K]3 years ago
8 0

we have

f(x)=-(x+3)(x-1)

f(x)=-(x^{2} -x+3x-3) \\ \\f(x)=-(x^{2} +2x-3)\\ \\f(x)=-x^{2}-2x+3

Convert into vertex form

Group terms that contain the same variable, and move the constant to the opposite side of the equation

f(x)-3=-(x^{2}+2x)

Complete the square. Remember to balance the equation by adding the same constants to each side

f(x)-3-1=-(x^{2}+2x+1)

f(x)-4=-(x^{2}+2x+1)

Rewrite as perfect squares

f(x)-4=-(x+1)^{2}

f(x)=-(x+1)^{2}+4 -------> equation in vertex form

This is the equation of a vertical parabola open down

The vertex is a maximum---------> (-1,4)

therefore

the domain of the function is the interval---------> (-∞,∞)

Domain is all real numbers

The range of the function is the interval --------> (-∞,4]

Range is all real number less than or equal to 4

Using a graphing tool

see the attached figure to better understand the problem


rosijanka [135]3 years ago
3 0
The domain is all real numbers.

The range is all real numbers less than or equal to 4.

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Basile [38]
4 is not a numerator up there I believeee
5 0
3 years ago
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3,0 and 4,l what is the y-intercept of the line
alexandr1967 [171]

Answer:

Step-by-step explanation:

(3,0),(4,1) ⇒ (x₁,y₁),(x₂,y₂)

to find the equation of the line

y-y₁= {(y₂-y₁)/(x₂-x₁)}(x-x₁)

y-0= [(1-0)/(4-3)] (x-3)

y-0 = 1/1(x-3)

y-0 = x-3

y= x-3+0

y=x-3

compare to y=mx+c, where m is the gradient and c is the intercept on y-axis

m=1, c=-3

∴the y-intercept of the line is -3

7 0
3 years ago
What is the property of 21 times 9 = 9 times 21
zaharov [31]
21 x 9 = 9 x 21 is the commutative property.
6 0
3 years ago
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Which similarity statements are true? Check all that apply. △JKL ~ △KML △JKM ~ △JKL △JKM ~ △KML △JMK ~ △JKL △JMK ~ △KML
Aliun [14]
The answer:

according to the image, the main theorem concerning right triangle similarity is as follow:
the altitude to the hypotenuse of a right triangle divides the triangle into two triangles that are similar to the original triangle and each other, 

in our case, KL is the altitude, and by applying theorem, we get three triangles that are similar:
therefore:
<span>△JKL ~ △JKM
</span><span>△JKM ~ △JKM
</span><span>△JMK ~ △KML</span>
5 0
3 years ago
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Solve for the inequality -1/3v -2&lt;5
polet [3.4K]

Answer:

v > -21

Step-by-step explanation:

-1/3v - 2 < 5

add 2

-1/3v < 7

multiply by -3

(if negative, switch sign)

v  > -21

3 0
3 years ago
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