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ratelena [41]
3 years ago
13

Describe the graph of the function f(x) = x3 − 11x2 + 36x − 36. Include the y-intercept, x-intercepts, and the shape of the grap

h.
Mathematics
1 answer:
kap26 [50]3 years ago
3 0
1) y-intercept => x = 0, => y = f(0) = 0 - 0 + 0 - 36 = -36

2) x-intercept => y = 0 => factor the function (start by dividing by x -2)

f(x) = (x-2)(x-3)(x-6) =0 => x =2, x = 3, x = 6 (these are the x-intercepts)

3) critical points:

between x = 2 and x = 3, there is a local maximum

between x =3 and x = 6 there is a local minimum

3) Shape.

The function comes growing from - infinity.

In the third quadrant the function is negative (it does not pass throuhg the second quadrant)

It enters to the fourth quadrant intercepting the y-axis at y = -36. It continues growing and intercepts the x-axis at x = 2.

 It continues increasing until a maximum local positive value, starts to decrease, intercepts the x-axis at x = 3, continues decreasing, becomes negative, gets a local minimum in the fourth quadrant, starts to increase, intercepts the x-axis at x = 6, becomes positive, and continues growing.
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(TEN POINTS)
Rainbow [258]
F(-1)= -3 is (-1,-3) and f(2) = 6 is (2,6) where f(x) = y
y=mx + b is the slope-intercept form whereas m equals the slope (rate of change) and b equals the y-intercept (initial amount/what y is when x is 0.)

First, we need to find the slope between the two points (-1,-3) and (2,6). To find the slope we could use one of it's formulas \frac{y^2 - y^1}{x^2 - x^1}.  
1. (-1,-3)
2. (2,6)
\frac{6 - -3}{2 - -1} → \frac{9}{3} → \frac{3}{1}

The slope is 3 (\frac{3}{1}). Thusly, y = 3x + b

To find out the y-intercept, we can reverse the slope. [Note: This \frac{3}{1} is in \frac{rise}{run} where rise is 'y' and run is 'x'. Reversed would be \frac{-3}{-1} ]. Take the second ordered pair and use our reversed slope on it until we get 0 for x. 

(2, 6) ⇒ (2 - 1, 6 -3) ⇒ (1, 3) ⇒ (0,0)

Y-intercept is 0. Therefore, y= 3x + 0 [NOTE: y = f(x), so if you want it in function notation form it's just f(x) = 3x + 0.]
6 0
3 years ago
X-3/18=12/9<br> what is the answer? It is proportions.
olga nikolaevna [1]

Answer:

x=3/2

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
Which equation can pair with 3x + 4y = 8 to create a consistent and independent system?
Hunter-Best [27]
There isn't any choices given in this problem but I can give you a tip to answer these kinds of problem. When you say independent, it means that the equation cannot be algebraically altered to result to 3x + 4y = 8. So the equation 6x + 8y = 16 is not an independent equation since when you divide each side by 2 it will result to 3x + 4y =8. You get the idea. <span />
6 0
3 years ago
PLEASE HELPPPPP PLEAAASEE
nata0808 [166]

Answer:

11%

Step-by-step explanation:

The full circle graph represents 100% of the given population. All populations are given except for "three or more." Adding all percentages of each population should add up to 100%.

No absences (none): 23%

One absence: 45%

Two absences: 21%

Three more absences: unknown.

Let the variable x represent the unknown population.

23% + 45% + 21% + x = 100%

Combine like terms.

89% + x = 100%

Subtract 89% from both sides.

x = 11%

To put it more simply, subtract all the percentages from 100% to get the percent of the missing population. 100 - 23 - 45 - 21 = 11

7 0
3 years ago
Read 2 more answers
The population of a small town can be modeled by the equation where t is the number of years since the collection of the populat
liberstina [14]

The true statements is the population was 4800 when the collection of data began. (3rd option)

<h3>What is an exponential function?</h3>

An exponential equation can be described as an equation with exponents. The exponent is usually a variable.

The general form of exponential equation is f(x) = e^{x}

Where:

  • x = the variable
  • e = constant

When a population grows at an exponential rate, it usually has compound rate of growth. Compound growth refers to the geometric progression of a variable.

The exponential equation used to represent an exponential growth usually have this form:

FV = PV (1 + r)^n

Where:

  • FV = future population
  • PV = present population
  • r = rate of growth
  • n = number of years

Given this exponential equation : f(x) = 4800 (1.02)^t

  • 4800 = initial population or population when the data collection began
  • 2 % = rate of growth
  • t = number of years

To learn more about exponential functions, please check: brainly.com/question/26331578

#SPJ1

7 0
1 year ago
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