Say whether each of these statements about square numbers is always true, sometimes true or never true

f(x)=x^2; vertical shrink by a factor of 1/2 and a reflection in the y-axis, followed by a translation 1 unit down

NeX [460]

The image of the function f(x) after vertical shrink by a factor of 1/2

and a reflection in the y-axis, followed by a translation 1 unit down

is g(x) = $\frac{1}{2}$ x² - 1

Step-by-step explanation:

Lets revise:

1. The vertical shrink

A vertical shrinking is the squeezing of the graph toward the x-axis.

if 0 < k < 1 (a fraction), the graph of y = k•f(x) is the graph of f(x) vertically

shrunk by multiplying each of its y-coordinates by k

2. The reflection

If the function f(x) reflected across the y-axis, then its image is g(x) = f(-x)

3. Vertical translation

If the function f(x) translated vertically up by m units, then its image

is g(x) = f(x) + m

If the function f(x) translated vertically down by m units, then its image

is g(x) = f(x) - m

Now let us solve the problem

∵ f(x) = x²

∵ f(x) shrunk by a factor of $\frac{1}{2}$

∴ The image of f(x) = $\frac{1}{2}$ x²

∵ The image of f(x) reflected across y-axis

∴ The sign of x will change

∴ The new image of f(x) = $\frac{1}{2}$ (-x)²

∵ The new image of f(x) translated 1 unit down

∴ We will subtract the new image of f(x) by 1

∴ The last image of f(x) is g(x) = $\frac{1}{2}$ (-x)² - 1

(-x)² = x² because even exponents reject the negative sign

The image of the function f(x) after vertical shrink by a factor of 1/2

and a reflection in the y-axis, followed by a translation 1 unit down

is g(x) = $\frac{1}{2}$ x² - 1

The attached graph for more understand

Learn more:

you can learn more about transformation in brainly.com/question/2415963

#LearnwithBrainly

4 0

3 years ago

PLEASE ANSWER THIS

kumpel [21]

(30 0Z less then) is your answer :)

6 0

3 years ago

Read 2 more answers

#3 Can someone please help me with these questions!!!!

rosijanka [135]

Answer:

Option A 90,68

$m\angle 1=90^o$

$m\angle 2=68^o$

Step-by-step explanation:

see the attached figure to better understand the problem

The figure shows a kite

we know that

A kite properties include

1) two pairs of consecutive, congruent sides

2) congruent non-vertex angles

3) perpendicular diagonals

Find the measure of angle 1

we have that

$m\angle 1=90^o$ ----> by the diagonals are perpendicular

Find the measure of angle 2

we know that

triangle AEB is congruent with triangle CEB

so

$m\angle EAB=m\angle ECB=m\angle 2$

In the right triangle EAB

$m\angle EAB+22^o=90^o$ ----> by complementary angles in a right triangle

so

$m\angle EAB=90^o-22^o=68^o$

therefore

$m\angle 2=68^o$

7 0

3 years ago

20 POINTS! WILL MAKE BRAINLIEST

SVETLANKA909090 [29]

1.a sphere with a radius of three units

By definition, the volume of a sphere is:
$V = ( \frac{4}{3} ) (\pi) (r ^ 3)
$
Substituting values we have:
$V=(\frac{4}{3})(\pi)(3^3)$
Rewriting we have:
$V = (4) (\pi) (3 ^ 2)

V = (4) (\pi) (9)

V = 36\pi$

2.a cone with a diameter of twelve units and a height of three units

By definition, the volume of a cone is given by:
$V = \frac{1}{3} (\pi) (r ^ 2) (h)
$
Substituting values we have:
$V = \frac{1}{3} (\pi) ((\frac{12}{2}) ^ 2) (3)
$
Rewriting we have:
$V = (\pi) (6 ^ 2)

V = 36\pi$

6 0

3 years ago

ms.halquist and 3 friends went to eat sushi.The meal cost 45$ and they paid waitress a 15%tip .how much was the bill?

brilliants [131]

Answer: 51.75$

Step-by-step explanation: First, turn 15% into the decimal 0.15, then multiply by 45, which equals 6.75. Now add 6.75, which is the amount the waitress got tipped to 45, which equals 51.75$ total.

5 0

2 years ago