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Ann [662]
3 years ago
6

write the given equation into vertex form and sketch the graph. Determine the domain and range f(x)=3x^2-6+2 plss help

Mathematics
1 answer:
LuckyWell [14K]3 years ago
4 0

Answer: the range would thus be [-3, 1/3].)

Step-by-step explanation:

1. To sketch the function f(x) = (2/3)x - 3, we first need to find two points that we can later join to sketch the line, for example the x- and y-intercepts.

a) The x-intercept occurs when f(x) = 0, so if f(x) = 0, then:

f(x) = (2/3)x - 3

0 = (2/3)x - 3

3 = (2/3)x (Add three to both sides)

3*(3/2) = x (Multiply both sides by 3/2)

9/2 = x

We have now found the x-intercept at (9/2, 0)

b) The y-intercept occurs when x = 0, so:

f(x) = (2/3)x - 3

f(0) = (2/3)*0 - 3

f(0) = -3

Now we know that the y-intercept is at (0, -3)

c) All that's left is to sketch the graph axes and label them, plot the two points, join them together using a ruler and label their coordinates.

2. The Domain is the range of x-values for which the function exists, and the Range is the range of y-values for which the function exists.

Since there haven't been any constraints specified, we can say that both the Domain and Range are (-∞, ∞), since the graph continues forever both along the x- and y-axis.

(Note that this isn't always the case and would change if, for example, the question stipulated that there was a domain of [0, 5] and you had to find the range. Then, you would calculate the value of y at each end of the domain (if x = 0, y = -3 and if x = 5, y = 1/3) - in my example, the range would thus be [-3, 1/3].)

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3 years ago
Connecticut families were asked how much they spent weekly on groceries. Using the following data, construct and interpret a 95%
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Answer:

The 95% confidence interval for the population mean amount spent on groceries by Connecticut families is ($73.20, $280.21).

Step-by-step explanation:

The data for the amount of money spent weekly on groceries is as follows:

S = {210, 23, 350, 112, 27, 175, 275, 50, 95, 450}

<em>n</em> = 10

Compute the sample mean and sample standard deviation:

\bar x =\frac{1}{n}\cdot\sum X=\frac{ 1767 }{ 10 }= 176.7

s= \sqrt{ \frac{ \sum{\left(x_i - \overline{x}\right)^2 }}{n-1} }       = \sqrt{ \frac{ 188448.1 }{ 10 - 1} } \approx 144.702

It is assumed that the data come from a normal distribution.

Since the population standard deviation is not known, use a <em>t</em> confidence interval.

The critical value of <em>t</em> for 95% confidence level and degrees of freedom = n - 1 = 10 - 1 = 9 is:

t_{\alpha/2, (n-1)}=t_{0.05/2, (10-1)}=t_{0.025, 9}=2.262

*Use a <em>t</em>-table.

Compute the 95% confidence interval for the population mean amount spent on groceries by Connecticut families as follows:

CI=\bar x\pm t_{\alpha/2, (n-1)}\cdot\ \frac{s}{\sqrt{n}}

     =176.7\pm 2.262\cdot\ \frac{144.702}{\sqrt{10}}\\\\=176.7\pm 103.5064\\\\=(73.1936, 280.2064)\\\\\approx (73.20, 280.21)

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If the numerator and denominator of the fraction is increased by 2an1 respectively; it becomes3/4 if the numerator and the denom
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Answer:

The fraction is\frac{7}{1}

Step-by-step explanation:

Let the numerator be x and denominator be y

So, Fraction = \frac{x}{y}

Now we are given that numerator and denominator of the fraction is increased by 2 and 1 respectively. it becomes 3/4

So, Fraction becomes :\frac{x+2}{y+1}=\frac{3}{4}

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So, Fraction = \frac{x}{y}=\frac{7}{1}

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