All categories

3 years ago

For the following exercises, evaluate the function at the indicated values: f (−3); f (2); f (−a); −f (a); f (a + h).

Mathematics

1 answer:

ser-zykov [4K]3 years ago

3 0

Answer:

5. f(x) = -2x² + 3x

f(-3) = -2(-3)² + 3(-3) = -27

f(2) = -2(2)² + 3(2) = -2

f(-a) = -2(-a)² + 3(-a) = -2a² - 3a

-f(a) = -[-2a² + 3a] = 2a² - 3a

f(a + h) = -2(a + h)² + 3(a + h) = -2(a² + 2ah + h²) + 3a + 3h = -2a² - 4ah - 2h² + 3a + 3h

6. f(x) = 2|3x - 1|

f(-3) = 2|3(-3) - 1| = 2*10 = 20

f(2) = 2|3(2) - 1| = 2*5 = 10

f(-a) = 2|3(-a) - 1| = 2|-3a - 1|

-f(a) = -(2|3a - 1|) = -2|3a - 1|

f(a + h) = 2|3(a + h) - 1| = 2|3a + 3h - 1|

You might be interested in

A circle has a diameter with endpoints at (6, 5) and (8, 5). Write the equation for the circle.

mario62 [17]

Answer:

$(x-7)^2+(y-5)^2=1$

Step-by-step explanation:

The two things that are required to formulate the equation of the circle is the center coordinate and the radius of the circle!

Center of the circle:

The center of the circle always lies at the midpoint of the endpoints of its diameter: Let's call the endpoints A(6,5) and B(8,5).

Using the midpoint formula we'll get:

$(x_m, y_m) = \left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)$

$(x_m, y_m) = \left(\dfrac{6+8}{2},\dfrac{5+5}{2}\right)$

$(x_m, y_m) = (7,5)$

This is the center coordinate of our circle.

Radius:

The radius of the circle is the distance from the center of the circle to any of the endpoints of the diameter (A or B)

We can use the distance formula:

$r = \sqrt{(x_1-x_2)^2+(y_1-y_2)^2}$

$r = \sqrt{(x_1-x_m)^2+(y_1-y_m)^2}$

$r = \sqrt{(6-7)^2+(5-5)^2}$

$r = \sqrt{1^2}$

$r = 1$

Equation of the circle:

The equation is written as:

$(x-a)^2+(y-b)^2=r^2$

here, (a,b) are the center points of the circle

in our case this is $(a,b)=(x_m,y_m)=(7,5)$

and r = 1

$(x-7)^2+(y-5)^2=1^2$

$(x-7)^2+(y-5)^2=1$

This is the equation of the circle!

3 0

3 years ago

. Byron has 17 kilograms of black pepper. He uses a of the pepper

Sphinxa [80]

About 2.43 kg of pepper
Divide 17 by 7

5 0

3 years ago

Clinton decided to by 300 shares of stock in a electronics company.Each share costs $60.Which of the following could he use to f

REY [17]

$60.00×300=18,000 ..............

3 0

3 years ago

Given that f:x→ax+b and f²:x→4x+9, find the value of the constants a and b

zimovet [89]

Answer:

Step-by-step explanation:

hello :

ax+b =4x+9 so a=4 and b=9

4 0

4 years ago

Which system of equations does not have a real solution

Aloiza [94]

Answer:

the correct answer is y = x 2 + 3x - 5 and x + y = -10

Step-by-step explanation:

5 0

4 years ago