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2 years ago

What value of k transforms the graph of f(x)=0.5x+3 into graph g? Describe the transformation.

Mathematics

1 answer:

lozanna [386]2 years ago

8 0

Using translation concepts, the values of k are given as follows:

7. k = 3.

8. k = -2.

9. k = 2.

<h3>What is a translation?</h3>

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

In this problem:

In graph 7, g(x) is a shift up of 3 units of f(x), hence k = 3.

In graph 8, g(x) is a shift left of 2 units of f(x), that is, g(x) = f(x + 2), hence k = -2.

In graph 9, g(x) is a vertical stretch by a factor of 2 of f(x), that is, g(x) = 2f(x), hence k = 2.

More can be learned about translation concepts at brainly.com/question/27885240

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As part of a new advertising campaign, a beverage company wants to increase the dimensions of their cans by a multiple of 1.12.

olga_2 [115]

Answer:

The new can can hold upto volume of 476.69 cubic centimeters.

Step-by-step explanation:

Diameter of the can = d = 6 cm

Radius of the can = r = 0.5d = 0.5 × 6 cm = 3 cm

Height of the can = h = 12 cm

Company wants to increase the dimensions of their cans by a multiple of 1.12. So, the new dimension will be:

r'= 3 cm × 1.12 = 3.36 cm

h' = 12 cm × 1.12 =13.44 cm

Volume of the = can = V

Volume of a cylinder = $\pi r^2h$

$V=\pi r'^2h'$

$=3.14\times (3.36 cm)^2\times 13.44 cm=476.6808 cm^3\approx 476.68 cm^3$

The new can can hold upto volume of 476.69 cubic centimeters.

3 0

3 years ago

Suppose that the functions r and s are defined for all real numbers x as follows.

mixas84 [53]

ANSWER

Given

$r(x) = x - 1$

and

$s(x) = 3 {x}^{2}$
ANSWER TO QUESTION 1

$(r + s)(x) = r(x) + s(x)$

$(r + s)(x) = x - 1 + 3 {x}^{2}$

$(r + s)(x) = 3 {x}^{2} + x - 1$

ANSWER TO QUESTION 2

$(r \times s)(x) = r(x) \times s(x)$

$(r \times s)(x) = (x - 1) \times 3 {x}^{2}$

$(r \times s)(x) = 3 {x}^{3} - 3 {x}^{2}$

ANSWER TO QUESTION 3

$( r - s)(x) = r(x) - s(x)$

$( r - s)(x) = x - 1 - 3 {x}^{2}$

$( r - s)( - 3) = (- 3) - 1 - 3 ({ - 3}^{2} )$

$( r - s)( - 3) = - 4 - 3 \times 9$

$( r - s)( - 3) = - 4 - 27 = - 31$

4 0

3 years ago

Which graph represents a vertical translation by 4 units down of the function f(x)=2x?

KATRIN_1 [288]

F(x)=2x-4

4 units DOWN would mean that the k-value is -4, which is put at the very end of the equation. hope this helped!

3 0

3 years ago

I need a help please

asambeis [7]

Answer:

Step-by-step explanation:

1+2->12^-4=1243