Please help me out with this one! I need step by step instructions (30 points!)

Which figure correctly demonstrates using a straight line to determine that the graphed equation is not a function of x?

Ulleksa [173]

Answer:

Lower left.

Step-by-step explanation:

To determine if a graph is a function the "vertical line test is used. If any point on a graph has one x value go to two y values it is not a function.

Witht he four pictures, the two on the right use a horizontal line, so it doesn't tell at all, on the leftthe upper one is vertical but it doesn't show that one x value has two corresponding y values. So it must be the lower left one.

The lower left picture has a line at x=1, and it passes through the line of the graph at two different y values, 4 and -4. So this has two y values with one x value.

3 0

3 years ago

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hi:) my teacher taught another method but she said we’ll only be learning it next year. I didn’t understand it , anyone able to

vfiekz [6]

Answer:

Differentiation can be used to find the gradient of the graph at a particular point.

To differentiate,

- bring down the power

- power minus 1

Differentiating y with respect to x term would be written as $\frac{dy}{dx}$

Bringing down the power means to multiply the digit in the power to the equation first.

Let me show you an example.

$y = 5x^{2}$

$\frac{dy}{dx} = 2(5x^{2 - 1} ) \\ \frac{dy}{dx} = 10x^{1} \\ \frac{dy}{dx} = 10x$

Hence the gradient of the graph y=5x² at any point is given by the formula of 10x.

So at x=2,

gradient of graph is 10(2)= 20

Knowing the gradient, you can now find 2 points to plot your tangent using the gradient formula:

$\frac{y1 - y2}{x1 - x2}$

Let's look at example 3 again.

In this case, the graph is y=x³.

① Differentiate y with respect to x

$\frac{dy}{dx} = 3(x^{3 - 1} ) \\ \frac{dy}{dx} = 3 {x}^{2}$

② Find the value of the gradient at the point given.

When x=2,

$\frac{dy}{dx} = 3(2)^{2} \\ \frac{dy}{dx} = 3(4) \\ \frac{dy}{dx} = 12$

This means that the gradient of the tangent at x=2 is 12.

So at x=2, y=8

Let y2 be 8 and x2 be 2.

Subst into the gradient formula:

$\frac{y1 - 8}{x1 - 2} = 12 \\ y1 - 8 = 12(x1 - 2) \\ y1 - 8 = 12x1 - 24 \\ y1 = 12x1 - 24 + 8 \\ y1 = 12x1 - 16$

Now you have an equation which shows how any coordinates that lie on the tangent are related to each other.

Use this to find 2 coordinates so you can draw a line through them to draw the tangent.

When x=3,

y= 12(3) -16

y= 36 -16

y= 20

when x= 1.5,

y= 12(1.5) -16

y= 2

Plot these 2 points: (3 ,20) and (1.5, 2)

Now draw the tangent through these 2 points.

Let's check:

$gradient = \frac{20 - 2}{3 - 1.5} \\ gradeint = \frac{18}{1.5} \\ gradient = 12$

Essentially, what we are trying to achieve is an accurate gradient value. However, we are not allowed to use differentiation ( Sec 4 A Math syllabus ) to answer the question. So use that as a side working to achieve an accurate tangent or you can also use that to check if your answer is close to the correct answer.

If the equation is y= x³-12 instead,

note that you have to differentiate x³ just like in example 3, ignoring the -12 since <u>differentiating a constant would give you zero</u>.

Further explanation:

Constants are basically _x⁰.

3= 3x⁰

4= 4x⁰

This is because x⁰= 1.

So if we differentiate 3,

we get d/dx (3x⁰)= 0(3x^-1)

This would give us 0 since anything multiplied by 0 is still 0.

6 0

3 years ago

A company sells artwork using a website. Information about the number of people that

VARVARA [1.3K]

The probability that the next person that visits the website will purchase more than 1 piece of artwork is $\frac{3}{50}$ .

Step-by-step explanation:

Step 1; The probability of an event is given by dividing the number of favorable outcomes i.e. the number of people that brought more than one piece of artwork by the total number of outcomes i.e. the total number of people that visited the website.

Step 2; The probability is calculated by the following values;

The number of favorable outcomes = the number of people that purchased more than one piece of artwork = 9

The total number of outcomes = The number of people that did not buy any artwork + the number of people that brought one piece of artwork + the number of people that brought more than one piece of artwork

= 117 + 24 + 9 = 150.

The probability that the next person that visits the website will purchase more than 1 piece of artwork = $\frac{9}{150}$ = $\frac{3}{50}$ .