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3 years ago

What transformation has changed the parent function f(x) = log2x to its new appearance shown in the graph below?

Mathematics

1 answer:

Darina [25.2K]3 years ago

4 0

Answer: First Option

−2 • f(x)

Step-by-step explanation:

The function $y=log_2(x)$ passes through point (2,1) since the exponential function $2 ^ x = 2$ when $x = 1$ .

Then, if the transformed function passes through the point (2, -2) then this means that f(x) was multiplied by a factor of -2. So if an ordered pair $(x_0, y_0)$ belonged to f(x), then $(x_0, -2y_0)$ belongs to the transformed function. Therefore, if $f(x) = log_2 (x)$ passed through point (2, 1) then the transformed function passes through point (2, -2)

The transformation that multiplies to f(x) by a factor of -2 is:

$y = -2 * f (x)$

and the transformed function is:

$y = -2log_2 (x)$

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The design for the palladium window shown includes a semicircular shape at the top. The bottom is formed by squares of equal siz

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Answer:

$(a)\ Area = 3765.32$

$(b)\ Area = 4773$

Step-by-step explanation:

Given

$A_1 = 169in^2$ --- area of each square

$Shade = 4in$

See attachment for window

Solving (a): Area of the window

First, we calculate the dimension of each square

Let the length be L;

So:

$L^2 = A_1$

$L^2 = 169$

$L = \sqrt{169$

$L=13$

The length of two squares make up the radius of the semicircle.

So:

$r = 2 * L$

$r = 2*13$

$r = 26$

The window is made up of a larger square and a semi-circle

Next, calculate the area of the larger square.

16 small squares made up the larger square.

So, the area is:

$A_2 = 16 * 169$

$A_2 = 2704$

The area of the semicircle is:

$A_3 = \frac{\pi r^2}{2}$

$A_3 = \frac{3.14 * 26^2}{2}$

$A_3 = 1061.32$

So, the area of the window is:

$Area = A_2 + A_3$

$Area = 2704 + 1061.32$

$Area = 3765.32$

Solving (b): Area of the shade

The shade extends 4 inches beyond the window.

This means that;

The bottom length is now; Initial length + 8

And the height is: Initial height + 4

In (a), the length of each square is calculated as: 13in

4 squares make up the length and the height.

So, the new dimension is:

$Length = 4 * 13 + 8$

$Length = 60$

$Height = 4*13 + 4$

$Height = 56$

The area is:

$A_1 = 60 * 56 = 3360$

The radius of the semicircle becomes initial radius + 4

$r = 26 + 4 = 30$

The area is:

$A_2 = \frac{3.14 * 30^2}{2} = 1413$

The area of the shade is:

$Area = A_1 + A_2$

$Area = 3360 + 1413$

$Area = 4773$

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