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3 years ago

Which statement correctly describes the relationship between the graph of f(x) and g(x)=f(x+2) ?

Mathematics

2 answers:

Nutka1998 [239]3 years ago

7 0

Answer:

The graph of g(x) is the graph of f(x) translated 2 units left

Step-by-step explanation:

coldgirl [10]3 years ago

4 0

Answer:

The graph of g(x) is the graph of f(x) translated 2 units left.

Step-by-step explanation:

When a change is made inside the parenthesis to the input, the function shifts left and right. Addition shifts it left while subtraction shifts it to the right. Here it is translated two units to the left.

Example: f(x) = x $f(x+2) = x_{n+2}$

f(5) = 5 x+2 = 5

x+2-2 = 5-2

x=3 and f(3) = 3

f(5) = 3

This is so because 5 now matches to the output of two previous which is 3.

You might be interested in

How do I find the 5 roots of 1^(1/5) using De Moivre's Theorem?

cupoosta [38]

Do you mean the 5th roots of 1? Or the 5th roots of 1^(1/5), i.e. the 5th roots of the 5th roots of 1?

I assume you mean the former. To begin with,

1 = exp(0°i ) = cos(0°) + i sin(0°)

Take the 5th root, i.e. (1/5)th power of both sides, so that by DeMoivre's theorem,

1^(1/5) = [ cos(0°) + i sin(0°) ]^(1/5)

1^(1/5) = cos((0° + 360°n)/5) + i sin((0° + 360°n)/5)

where n = 0, 1, 2, 3, or 4. Then 1^(1/5) has the 5 possible values,

• cos(0°/5) + i sin(0°/5) = 1

• cos(360°/5) + i sin(360°/5) = cos(72°) + i sin(72°)

• cos(720°/5) + i sin(720°/5) = cos(144°) + i sin(144°)

• cos(1080°/5) + i sin(1080°/5) = cos(216°) + i sin(216°)

• cos(1440°/5) + i sin(1440°/5) = cos(288°) + i sin(288°)

If you wish, or are required to, you can go on to write these in terms of radicals by expanding cos(5x) and sin(5x) (where x = 72° so that 5x = 360°). For example,

cos(5x) = cos⁵(x) - 10 cos³(x) sin²(x) + 5 cos(x) sin⁴(x)

cos(5x) = cos⁵(x) - 10 cos³(x) (1 - cos²(x)) + 5 cos(x) (1 - cos²(x))²

cos(5x) = 16 cos⁵(x) - 20 cos³(x) + 5 cos(x)

which follows from the expansion

(cos(x) + i sin(x))⁵ = cos(5x) + i sin(5x)

due to DeMoivre's theorem and equating the real parts. Then cos(5x) = 1, and you can try to solve for cos(x) :

1 = 16 cos⁵(x) - 20 cos³(x) + 5 cos(x)

Actually, it would be easier to find sin(x) first, since sin(5x) = 0. The expansion in terms of sin(x) will look quite similar to the one shown here.

4 0

3 years ago

In the summer reading program, a participant earns 50 stars for reading 10 books. The library tracks the number of stars(y, vert

melamori03 [73]

Answer:

C: Point(0,50) Represents the unit rate

Step-by-step explanation:

8 0

3 years ago

The distance between the front wheels of a model car is 4.5 centimeters. What is the actual distance on the car if the scale is

Kamila [148]

Answer:

108

Steps:

24 x 4.5 = 108

3 0

3 years ago

Use a t-test to test the claim about the population mean at the given level of significance using the given sample statistics.

Sonja [21]

Complete question is;

Use a t-test to test the claim about the population mean μ at the given level of significance α using the given sample statistics. Assume the population is normally distributed.

Claim: μ ≥ 8300,α= 0.10

Sample statistics: ¯x = 8000, s = 440, n = 24

a. What are the null and alternative hypotheses?

b. What is the value of the standardized test statistic? (Round to 2 decimal places as needed.)

c. What is the p-value? (Round to three decimal places as needed.)

d. Decide whether to reject or fail to reject the null hypothesis.

Answer:

A) Null hypothesis:H0: μ ≥ 8300

Alternative Hypothesis:Ha:μ < 8300

B) t = -3.34

C) p-value = 0.001

D) we will reject the null hypothesis

Step-by-step explanation:

A) We are told that the claim is: μ ≥ 8300. Thus, the null hypothesis would be the claim. So;

Null hypothesis:H0: μ ≥ 8300

Also, alternative hypothesis would be;

Alternative Hypothesis:Ha:μ < 8300

B)Formula for standardized test statistic with a t-test is;

t = (¯x - μ)/√(s/n)

Plugging in the relevant values, we have;

t = (8000 - 8300)/√(440/24)

t = -3.34

C) From online p-value from t-score calculator attached using t = -3.34, n = 24, significance level = 0.01, DF = 24 - 1 = 23 and a one - tailed test, we have;

p-value = 0.001421 ≈ 0.001

D) The p-value of 0.001 is less than the significance value of 0.01,thus we will reject the null hypothesis