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makkiz [27]
3 years ago
14

Consider the function f(x) = ex and the function g(x), which is shown below. How will the graph of g(x) differ from the graph of

f(x)?

Mathematics
1 answer:
SIZIF [17.4K]3 years ago
6 0

Answer: Option C

Step-by-step explanation:

If the graph of the function g(x)=f(x) +b  represents the transformations made to the graph of y= f(x)  then, by definition:

If b> 0 the graph moves vertically upwards.

If b the graph moves vertically down

In this problem we have the function g(x)=e^x+5 and our parent function is f(x) = e^x

therefore it is true that b =5 > 0

Therefore the graph of f(x)=e^x is moves vertically upwards by a factor of 5 units.

The answer is the Option C:  "The graph of g(x) is the graph of f(x) shifted up 5 units"

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Engineers must consider the diameters of heads when designing helmets. The company researchers have determined that the populati
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Answer:

1. The minimum head breadth that will fit the clientele is of 3.95-in.

2. The maximum head breadth that will fit the clientele is of 9.25-in.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

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Z = \frac{X - \mu}{\sigma}

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Mean of 6.6-in and a standard deviation of 1.1-in.

This means that \mu = 6.6, \sigma = 1.1

1. What is the minimum head breadth that will fit the clientele?

The 0.8th percentile, which is X when Z has a p-value of 0.008, so X when Z = -2.41.

Z = \frac{X - \mu}{\sigma}

-2.41 = \frac{X - 6.6}{1.1}

X - 6.6 = -2.41*1.1

X = 3.95

The minimum head breadth that will fit the clientele is of 3.95-in.

2. What is the maximum head breadth that will fit the clientele?

The 100 - 0.8 = 99.2nd percentile, which is X when Z has a p-value of 0.992, so X when Z = 2.41.

Z = \frac{X - \mu}{\sigma}

2.41 = \frac{X - 6.6}{1.1}

X - 6.6 = 2.41*1.1

X = 9.25

The maximum head breadth that will fit the clientele is of 9.25-in.

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