Analyze the function’s graph to determine which statement is true.

Given the parent function f(x)=x^2 in red, write the equation for the transformed function g(x) in green.

Nataly_w [17]

Answer:

g(x) = 2x² + 1

Step-by-step explanation:

The parabola got thinner, so to show that, you put a 2 before x² to show that the graph was dilated (or thinned) by a factor of 2 (Note: this number can also be negative, so if the dilation factor is negative, it's okay). Since the parabola shifts up by 1, you then add + 1 after x² to show the positive upward shift.

Your full equation would look like this: g(x) = 2x² + 1

Dilation: this just means that every point on the parent function was double (or whatever the factor is) in the transformed function.

5 0

2 years ago

Find the value of the derivative (if it exists) at the indicated extremum. (If an answer does not exist, enter DNE.)

Liono4ka [1.6K]

Answer:

The answer is "0".

Step-by-step explanation:

Please find the correct question in the attached file.

Given value:

$\to f(x) =\frac{x^2}{x^2+5}\\\\$

Formula:

$\bold{\frac{d}{dx} \frac{u}{v} = \frac{ v \frac{du}{dx} - u \frac{dv}{dx}}{v^2}}$

$\to f'(x) =\frac{(x^2+5) 2x -2x^3 (2x)}{(x^2+5)^2}\\\\\to f'(0) =\frac{(0^2+5)2(0) -4(0)^4}{(0^2+5)^2}\\\\\to f'(0) =\frac{(0)(5) -2(0)}{(5)^2}\\\\\to f'(0) =\frac{0 - 0}{(5)^2}\\\\\to f'(0) =\frac{0}{25}\\\\\to f'(0) = 0$

6 0

2 years ago

Why is this correct?

Vanyuwa [196]

Answer: A= independent variable W = dependent variable

Step-by-step explanation:

w= a/25

7 0

2 years ago

Write the slope-intercept form of the equation of each line

Vera_Pavlovna [14]

First let's talk about the blue line.

You can see its rising so its slope is certainly positive. But by how much is it rising? You can observe that each unit it rises it goes 1 forward and 1 up so its slope is the ratio of 1 up and 1 forward which is just 1.

We have thusly,

$y=x+n$

Now look at where blue line intercepts y-axis, -1. That is our n.

So the blue line has the equation of,

$y=x-1$

Next the black lines. The black lines are axes so their equations are a bit different.

First let's deal with x-axis, does it have slope? Yes but it is 0. The x-axis is still, not rising nor falling. Where does x-axis intercept y-axis? At 0. So the equation would be,

$y=0x+0=0$

Now we have y-axis. Does y axis have a slope? Yes but it is $\infty$ . The y-axis rises infinitely in no run. Where does it intercept y-axis? Everywhere! So what should the equation be? What if we ask where does y-axis intercept x-axis and write its equation in terms of x. Y-axis intercepts x-axis at 0 which means its equation is,

$x=0$

That is, every point of a form $(0,a)$ lies on y-axis.

Hope this helps :)

8 0

2 years ago

In most environments and cells themselves, there are

Salsk061 [2.6K]

Answer:

The cells membrane is selectively permeable, meaning only certain substances can easily pass through it. Only small, non polar molecules can easily pass through the small spaces between the hydrophobic heads and phospholipids. Water would have trouble due to it being a polar molecule. Proteins and carbs are quite large, making it difficult for them to pass through. Salt, which ionizes water, would also have difficulty passing through as it is a charged particle. Oxygen, on the other hand, is a non polar molecule that is small, so it can easily pass through the phospholipid bilayer.

Step-by-step explanation:

6 0

2 years ago