Resourcesdown chevron
Testimonials
Plans
Sign in
Sign up
Resourcesright arrow
Testimonials
Plans
Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Given the function f(x)=x^(2)+9x+12, determine the average rate of change of the function over the interval -5 <= x <= -1. Answer:

Given the function f(x)=x2+9x+12 f(x)=x^{2}+9 x+12 , determine the average rate of change of the function over the interval −5≤x≤−1 -5 \leq x \leq-1 .\newlineAnswer:

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Algebra 2right chevron icon
Average rate of changeright chevron icon

Full solution

Q. Given the function f(x)=x2+9x+12 f(x)=x^{2}+9 x+12 , determine the average rate of change of the function over the interval −5≤x≤−1 -5 \leq x \leq-1 .\newlineAnswer:
  1. Identify average rate of change formula: Identify the average rate of change formula, which is (f(b)−f(a))/(b−a)(f(b) - f(a)) / (b - a), where aa and bb are the endpoints of the interval.
  2. Calculate f(−5)f(-5): Calculate the value of f(−5)f(-5) by substituting x=−5x = -5 into the function f(x)=x2+9x+12f(x) = x^2 + 9x + 12.\newlinef(−5)=(−5)2+9∗(−5)+12f(-5) = (-5)^2 + 9*(-5) + 12\newlinef(−5)=25−45+12f(-5) = 25 - 45 + 12\newlinef(−5)=−8f(-5) = -8
  3. Calculate f(−1)f(-1): Calculate the value of f(−1)f(-1) by substituting x=−1x = -1 into the function f(x)=x2+9x+12f(x) = x^2 + 9x + 12.
    f(−1)=(−1)2+9∗(−1)+12f(-1) = (-1)^2 + 9*(-1) + 12
    f(−1)=1−9+12f(-1) = 1 - 9 + 12
    f(−1)=4f(-1) = 4
  4. Use average rate of change formula: Use the average rate of change formula with f(−5)=−8f(-5) = -8 and f(−1)=4f(-1) = 4.\newlineAverage rate of change = (f(−1)−f(−5))/(−1−(−5))(f(-1) - f(-5)) / (-1 - (-5))\newlineAverage rate of change = (4−(−8))/(−1+5)(4 - (-8)) / (-1 + 5)\newlineAverage rate of change = (4+8)/4(4 + 8) / 4\newlineAverage rate of change = 12/412 / 4\newlineAverage rate of change = 33

More problems from Average rate of change

Question
What is the domain of this function?\newline(9,–2)(6,–10)(–3,9)(5,2)(9,–2)(6,–10)(–3,9)(5,2)\newlineChoices:\newline(A){–3,5,6,9}(B){–10,–2,2,9}(C){2,5,6,9}(D){–6,–3,5,9}(A)\{–3,5,6,9\}\newline(B)\{–10,–2,2,9\}\newline(C)\{2,5,6,9\}\newline(D)\{–6,–3,5,9\}
Get tutor helpright-arrow

Posted 2 months ago

Question
Look at this set of ordered pairs:\newline(2,14)(2, 14)\newline(10,12)(10, 12)\newline(3,−19)(3, -19)\newlineIs this relation a function?\newlineChoices:\newline[[yes]\text{[[yes]}[no]]\text{[no]]}
Get tutor helpright-arrow

Posted 2 months ago

Question
Use the following function rule to find f(11) f(11) .\newlinef(x)=−10−7x f(x) = -10 - 7x \newlinef(11)= f(11) = _____
Get tutor helpright-arrow

Posted 2 months ago

Question
Find the slope of the line y=−3x−25 y = -3x - \frac{2}{5} .\newlineSimplify your answer and write it as a proper fraction, improper fraction, or integer.\newline_____\_\_\_\_\_
Get tutor helpright-arrow

Posted 2 months ago

Question
A line has a slope of 33 and passes through the point (−2,−10)(-2,-10). Write its equation in slope-intercept form.\newlineWrite your answer using integers, proper fractions, and improper fractions in simplest form.
Get tutor helpright-arrow

Posted 2 months ago

Question
What is the range of this function?\newliney = |x|\newlineChoices:\newlineall real numbers\text{all real numbers}\newline{y∣y≥0}\{y \mid y \geq 0\}\newline{y∣y≤0}\{y \mid y \leq 0\}\newline{y∣y>0}\{y \mid y > 0\}
Get tutor helpright-arrow

Posted 3 months ago

Question
Find g(x) g(x) , where g(x) g(x) is the translation 1 1 unit down of f(x)=∣x∣ f(x) = |x| .\newlineWrite your answer in the form a∣x−h∣+k a|x - h| + k , where a a , h h , and k k are integers.\newlineg(x)= g(x) = ______\newline
Get tutor helpright-arrow

Posted 3 months ago

Question
What is the domain of this function?\newline(8,–1)(7,–11)(–4,10)(4,3)(8,–1)(7,–11)(–4,10)(4,3)\newlineChoices: \newline(A){–4,4,7,8}(A)\{–4,4,7,8\}\newline(B){–11,–1,3,10}(B)\{–11,–1,3,10\}\newline(C){3,4,7,8}(C)\{3,4,7,8\}\newline(D){–7,–4,4,8}(D)\{–7,–4,4,8\}
Get tutor helpright-arrow

Posted 4 months ago

Question
What is the domain of this function?\newline(10, –3)(2, –9)(–5, 8)(3, 1)(10,\,–3)(2,\,–9)(–5,\,8)(3,\,1)\newlineChoices:\newline[{–5,2,3,10}][{–9, –3,1,8}][{1,2,3,10}][{–10, –5,2,3}][\{–5,2,3,10\}][\{–9,\,–3,1,8\}][\{1,2,3,10\}][\{–10,\,–5,2,3\}]
Get tutor helpright-arrow

Posted 2 months ago

Question
What is the domain of this function?\newline(1,–4)(9,–12)(–6,11)(7,5)(1,–4)(9,–12)(–6,11)(7,5)\newlineChoices:(A){–6,1,7,9}\newline\\(A)\{–6,1,7,9\}\newline(B){–12,–4,5,11}(B)\{–12,–4,5,11\}\newline(C{5,1,7,9}(C\{5,1,7,9\}\newline(D){–9,–6,1,7}(D)\{–9,–6,1,7\}
Get tutor helpright-arrow

Posted 2 months ago

View all (25)