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2 years ago

Describe how to transform the graph of f(x) = x2 to obtain the graph of the related function g(x).

Mathematics

1 answer:

olga55 [171]2 years ago

6 0

9514 1404 393

Answer:

left 1 unit
down 2 units

Step-by-step explanation:

The transformation g(x) = f(x -h) +k is a translation of f(x) to the right by h units and up k units.

1. h = -1, so the graph of g(x) is the graph of f(x) shifted left 1 unit. (blue)

2. k = -2, so the graph of g(x) is the graph of f(x) shifted down 2 units. (green)

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The ratio of boys to girls in Ella’s grade is 3 to 4. The ratio of boys to girls in Minh’s grade is 4 to 5. Each grade has a tot

Aneli [31]

Answer:

In mih's school there are 100 boys

While in Ella's school there are 80 boys

Step-by-step explanation:

X*1/5=20

X=100

X*1/4=20

X=80

4 0

2 years ago

Model the expression as groups of x + 2. There are x tiles. There are + 1 tiles. The equivalent expression is .

frez [133]

Answer:

x + 2 = 3

Step-by-step explanation:

x is always = to 1

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2 years ago

Read 2 more answers

Last year a banquet hall charged $65 per person to attend a function. The function C(p) = 65p represents the total cost, C, to r

zlopas [31]

Answer:

Domain = [0, 50]

Range = [0, 3250]

Step-by-step explanation:

A function shows the relationship between two variables (independent variable and dependent variable). The independent variable is a variable not dependent on any variable, it is the input of the function while the dependent variable is a variable dependent on other variable, it is the output of the function.

The domain of a function is the set of all input variables (independent variable) and the range of a function is the set of all output variables (dependent variables).

In the function C(p) = 65p, p is the independent variable and C(p) is the dependent variable.

Since the hall can hold a total of 50 people, the domain of the function = [0, 50]

C(0) = 65(0) = 0, C(50) = 65(50) = 3250

Hence, the range of the function = [0, 3250]

8 0

2 years ago

3. Find the slope of the line that passes through the pair of points.<br> (0, 0), (3,5)

Katena32 [7]

Answer:

5/3

Step-by-step explanation:

5 0

3 years ago

Evaluate the following integral using trigonometric substitution

serg [7]

Answer:

The result of the integral is:

$\arcsin{(\frac{x}{3})} + C$

Step-by-step explanation:

We are given the following integral:

$\int \frac{dx}{\sqrt{9-x^2}}$

Trigonometric substitution:

We have the term in the following format: $a^2 - x^2$ , in which a = 3.

In this case, the substitution is given by:

$x = a\sin{\theta}$

$dx = a\cos{\theta}d\theta$

In this question:

$a = 3$

$x = 3\sin{\theta}$

$dx = 3\cos{\theta}d\theta$

$\int \frac{3\cos{\theta}d\theta}{\sqrt{9-(3\sin{\theta})^2}} = \int \frac{3\cos{\theta}d\theta}{\sqrt{9 - 9\sin^{2}{\theta}}} = \int \frac{3\cos{\theta}d\theta}{\sqrt{9(1 - \sin^{\theta})}}$

We have the following trigonometric identity:

$\sin^{2}{\theta} + \cos^{2}{\theta} = 1$

$1 - \sin^{2}{\theta} = \cos^{2}{\theta}$

Replacing into the integral:

$\int \frac{3\cos{\theta}d\theta}{\sqrt{9(1 - \sin^{2}{\theta})}} = \int{\frac{3\cos{\theta}d\theta}{\sqrt{9\cos^{2}{\theta}}} = \int \frac{3\cos{\theta}d\theta}{3\cos{\theta}} = \int d\theta = \theta + C$

Coming back to x:

We have that:

$x = 3\sin{\theta}$

$\sin{\theta} = \frac{x}{3}$

Applying the arcsine(inverse sine) function to both sides, we get that:

$\theta = \arcsin{(\frac{x}{3})}$

The result of the integral is:

$\arcsin{(\frac{x}{3})} + C$

8 0

2 years ago