Use a graphing calculator to graph f (x) = -x³ + 2x? + 6x + 8 and find the following features of the graph. Round answers to the nearest hundredth, if necessary. List the x-intercept of the graph. x = |4| Find the local minimum of the graph. Find the local maximum of the graph. Find the intervals on which the function is decreasing. I< and > Find the interval on which the function is increasing. O

Q: For the function g(x) = (x-6)²-16, find each of the following by referring to the graph. (A)…

A: Here we have to find the given property.

Q: The graph of the function f(x) = 3x – x* + 5x? – 2x – 7 will behave like the graph of for large…

A:

Q: If f(x) = 2x2 + 5 and g(x) = 3x + a, find a so that the graph of f ∘ g crosses the y-axis at 23.

A: fx=2x2+5  &amp;  gx=3x+a Now, f∘gx=fgx=f3x+a=23x+a2+5

Q: Find the coordinates of points where the graph of f(x) = -x3 + 6x2 - 9x + 13 has horizontal…

A:

Q: Find the points of inflection and discuss the concavity of the graph of the function.

A:

Q: Find the points of inflection and discuss the concavity of the graph of the function. f(x) = −x3 +…

A: f(x)=-x3+6x2-5The given function is a continuous function…

Q: Let f(x) = -0.4x² + 7x-12. Find the x-coordinate of the vertex. Round your answer to 2 decimal…

A:

Q: Find the absolute maximum and minimum values of the following function on the given interval. Then…

A: Given that, gx=9-x2, -2≤x≤3 The absolute maximum or minimum of any function occurs at its critical…

Q: snip

A: Given function: fx=x2+2x-8

Q: Use the function f(x) to answer the questions. f(x) = −16x2 + 60x + 16 Part A: What are the…

A: Given   f(x) = -16x2+60x +16                     = -4 [4x2-15x -4]A.  To find x- intercept , put…

Q: The function f(x) = 3 - 4x - 2x2 is shown on this graph. f(x) 6 + 2 그 What value of at corresponds…

A:

Q: Describe the concavity of graph the of f(x)=(x–2)5/3 and find the points of inflection (if any).

A: We have to define concavity and find the points of inflection.

Q: If f(x) = 2x2 + 5 and g(x) = 3x + a, find a so that the graph of f ∘ g crosses the y-axis at 23

A: f(x)=2x2+5g(x)=3x+a

Q: Find the absolute maximum and minimum values of the function, if they exist, over the indicated…

A:

Q: Let f(x) = -0.4x² + 13x-12. Find the x-coordinate of the vertex. Round your answer to 2 decimal…

A:

Q: Suppose that f(x) = x2 + 2x - 8.(a) What is the vertex of f?(b) What are the x-intercepts of the…

A: (a) Given function is: fx=x2+2x-8 Let y = f(x) Then we get,…

Q: Given the function f (x) = x-12x +6: a) Find the intervals of increase or decrease, ( b) Find the…

A: f(x) = x4-12x3+6

Q: If exists, find the local maximum, minumum and inflection points of the function f(x)=…

A:

Q: Suppose that the​ x-intercepts of the graph of y=​f(x) are −7 and −4.

A:

Q: Suppose that f(x) = x ^ 2 + 4x - 21 (a) What is the vertex of f? (b) What are the x-intercepts of…

A: Vertex form of a quadratic function f(x) is given as below, f(x)=a(x-h)²+k and (h,k) is the vertex…

Q: Use a graphing calculator to graph f (x) = -r³ + x? + 8z + 10 and find the following features of the…

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Q: Find the points of inflection and discuss the concavity of the graph of the function.

A: Differentiate the function f(x)=-x3+6x2-5 with respect to x two times and carry out algebraic…

Q: Select the root(s) of the quadratic function f (x) = x2 + x - 6 -3 -2 -6 6 The y intercept point of…

A: We have to check

Q: Find the points of inflection and discuss the concavity of the graph of the function.

A: Given function is fx=2csc3x2 To find: The points of inflection and to determine concavity of the…

Q: Given the function f(x)=-2x' +3x² + 36x , a) Find the intervals of increase or decrease, . b) Find…

A: Answer to the question as follows:

Q: Given the function f(x) = –5/-1(x – 4) – 3 find the following: The vertex of the function is (0,0)…

A:

Q: Given the graph of f(x), solve a) f(x) > 0 and b) f(x) 0. O A. 5sxs7 O B. x 7 O C. 5 7 O D. 5sxs7

A: According to the given graph the function is: f(x) = (x - 6)2 - 1

Q: x²+7x Consider the graph of the function f (x) = x3 –5x²–14x' Where is the removable discontinuity?…

A: We will factor both numerator and denominator

Q: 3. For the graph of the function f(x) = x² – 20x + 102, find the following: a. Use completing the…

A: To Determine: for the graph of the following a) use completing the square to find the axis of…

Q: Given the following function: f(x)=-x^2+2x a) identify whether a maximum or minimum exists, c) find…

A: Please see the below picture for detailed solution.

Q: For the function: y = 0.01x- 0.001x² Find the zeros, the vertex and the optimum value (max. or min.)

A: As per company guideline we are supposed to solve only one question at a time. For other question…

Q: The function  y = 4 − 16x2  intersects the x-axis at the following values of x.

A: Consider the parabola equation y = 4-16x2. Remember that the yth coordinate of the points on the…

Q: Find the maximum or minimum value of the function.

A: Given function is fx=-x23+2x+7. To find the maximum or minimum value of the function. Solution:…

Q: Find the coordinates of points where the graph of f(x) = -x + 6x2 - 9x + 17 has horizontal tangents.…

A: topic - functions and derivatives

Q: Use the graph of g to solve: For what value of x is  g(x) = 1?

A: The graph of function is given.

Q: Use the leading-term test and your knowledge of y-intercepts to match the function with one of the…

A: Given the function fx=x5-x4+x2+3 To find out the graph of f(x) from the following options

Q: Consider the function g(x) = x² + 4x – What is the vertex of g ? The x -intercept(s) of g is/are…

A: First, we will convert the given equation into the vertex form by completing the squares.

Q: State whether f(x) has a maximum value or a minimum value, and find that value. f(x) = 2x2 – 4x – 2…

A:

Q: STATE whether the following function has maximum or a minimum. Determine the value of the maximum or…

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Q: Use the graph of y=f(x) to graph the given function. 4 y = f(x) -3 -2 -2- -3 -4- y=f(-x) 4. 3- 2-

A: Please see the below picture for detailed solution.

Q: g(x) = 2|x – 2|

A:

Q: Find the coordinates of points where the graph of f(x) = -x³ + 6x2 – 9x + 14 has horizontal…

A: The given function is Find the derivative of f(x) and equate it to zero.

Q: Use the x-intercepts to find the intervals on which the graph of f is above and below the x-axis.…

A:

Q: By expressing the function f(x) = 3x2 - 6x + 5 in the form of f(x) = a(x - p)2 + q, find the…

A: For the detailed solution of the problem follow the next step.

Q: Find the maximum or minimum value of the function. f(x) = 5 – 6x – x? Is this a maximum or minimum…

A: To find The maximum and minimum value of f(x) f(x)=5-6x-x^2

Q: Find the vertical asymptote (if any) of the graph of the function 2р + 3 (a) h(p) = р? — 49 7x (b)…

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Q: Find the absolute maximum value and the absolute minimum value, if any, of the function. (If an…

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Q: א b. S(x)- x² - 4 2

A: Use second derivative test

Q: 5. Find the maximum or minimum of the function, and state whether your answer is a maximum or…

A:

Q: Given the following function f(x)=-5 (x-3)^2+4 find the vertex, line of symmetry, and the minimum or…

A:

Transformation of Graphs

The word ‘transformation’ means modification. Transformation of the graph of a function is a process by which we modify or change the original graph and make a new graph.

Exponential Functions

The exponential function is a type of mathematical function which is used in real-world contexts. It helps to find out the exponential decay model or exponential growth model, in mathematical models. In this topic, we will understand descriptive rules, concepts, structures, graphs, interpreter series, work formulas, and examples of functions involving exponents.