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2 years ago

Which function is the result of vertically shrinking ƒ(x) = 2(x + 3)2 by a factor of ½ and reflecting it across the x-axis?

Mathematics

1 answer:

Gemiola [76]2 years ago

7 0

Answer:

C) y = -(x + 3)2

Step-by-step explanation:

To vertically shrink the function by a factor of 1/2, we just need to multiply f(x) by 1/2 (This way the values in the y-axis will decrease by a factor of 1/2):

$y = (1/2) * 2(x + 3)^2$

$y = (x + 3)^2$

Now, to reflect the function across the x-axis, we just need to put a minus sign in the front of the function (so the values in the first and second quadrant will go to the third and fourth quadrant, that is, f(x) will be -f(x)):

$y = -(x + 3)^2$

So the correct option is C)

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Use complete sentences to describe the range of the sine function.

MA_775_DIABLO [31]

The Range of a function is the set of all values that that function can take.

Given the sine function f(x)=sinx,

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According to the definition of the sine of an angle x in the unit circle,

$-1 \leq sinx \leq 1$ ,

so the sine of an angle is always larger or equal to -1, and smaller or equal to 1.

This means that the values that the sine function takes are any values between -1 and 1, inclusive.

This determines the Range of the sine function.

So the Range of the sine function is [-1, 1]

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2 years ago

Elliot collects miniature toy cars. He wants to fill 4 display cases.each display case holds 15 cars. He has 28 cars now, and he

baherus [9]

Answer:

Elliot has to wait 11 months before he has enough cars

Step-by-step explanation:

Elliot has 4 display cases with each case being able to hold 15 cars. Thus we know

total # of cars Elliot can place in his display case = 4 * 15 = 60 cars

From this, we can figure out how many more cars Elliot needs by subtracting the amount of cars he already has

# of cars Elliot needs = 60 - 28 = 32 cars

Now to find the number of months Elliot needs, we divide by how many he can buy each month

# of months Elliot needs to save up for = 32 / 3 = 10 2/3

Assuming Elliot does not get his allowance until the end of the month, we will have to round the number of months up to the nearest integer, 11

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2 years ago

In a sale, normal prices are reduced by 20%. Andrew bought a saddle for his horse in the sale. The sale price of the saddle was

pshichka [43]

The formula for this is: (sale price) / (1 - percentage)
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2 years ago

Solve for x in the equation ? 2x^2 +3 x-7 =x^2 +5x +39

otez555 [7]

Answer:

1 ± √47

Step-by-step explanation:

Combine like terms in 2x^2 +3 x-7 =x^2 +5x +39:

2x^2 - x^2 = x^2 (first term);

3x - 5x = -2x (second term);

-7 - 39 = -46 (third term)

Then we have, all on the left side, x^2 - 2x - 46, which is a quadratic equation. Here the coefficients are a = 1, b = -2 and c = -46.

Then the discriminant, b^2 - 4ac, is:

(-2)^2 - 4(1)(-46) = 4 + 184.

The roots are:

-(-2) ±√188 2 ± √4√47

------------------- = -------------------

2 2

= 1 ± √47 (last of the answer choices)

x = ------------------

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2 years ago

A bridge builder wants to know the width of a river. He stands at point A along the river. He picks a point C directly across th

Maurinko [17]

<span>width = 90 tan43 degrees = about 84 feet </span>

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2 years ago