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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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ohaa [14]

The equation can be used to find the time in hours, \dfrac{t}{4}+\dfrac{t}{7}=1 and the time will be 2.5 hours. So the correct answer is option A.

<h3>What is an equation?</h3>

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

Layna can paint a 350-square-foot room in 4 hours.It takes Bebe 7 hours to paint the same room.

Let t be the total time taken by both to paint.They are completing 1 job so the equation will be :

\dfrac{t}{4}+\dfrac{t}{7}=1

Further solving it we get;

7 t + 4 t = 28

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t = 2.5 hours.

Therefore the equation can be used to find the time in hours, \dfrac{t}{4}+\dfrac{t}{7}=1 and the time will be 2.5 hours. So the correct answer is option A.

To know more about equations follow

brainly.com/question/2972832

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IrinaK [193]
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Dafna1 [17]
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