What is the equation of the line passing through the vertices of the graphs of the functions f(x) = -x2-4x-3 and g(x) = 1/2x2-3x +5/2?

Q: How is the graph off (x) = x 3 - l2x 2 + 36x - 16 related to the derivative f'(x) = 3x 2 - 24x + 36?

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Q: What is an equation of the line that passes through the points (1,2) and (2,−1)? Put your answer in…

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Q: Which function has x-intercepts at −2π, −π, 0, π, 2π?

A: Given-  The function has its x- intercepts at -2pi, -pi, 0 , pi, 2pi

Q: Find the derivative of the function.

A: Given  g(x)=3x2-22x+3-2 g(x)=2x+33x2-22 g(x)=2x+323x2-22 We use the following and differentiate g(x)…

Q: What are the x- and y-intercepts of a function, and how are they found?

A: The x-intercept is the length from origin to where the graph of the function cut the x-axis.   The…

Q: What is the equation of the line through the point (-3 , 2) and has x intercept at x = -1?

A: Given: Line passes through ( -3,2) and has x intercept x=-1.   To find: Equation of the above line.…

Q: Find the derivative of the function f(x)=(2x-7)/(3x-2)

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Q: Find a linear function with slope - 3 that contains the point ( - 1, 4). Graph the function.

A: Our Aim is to find a linear function with slope -3 that contains thepoint (-1,4).Since, for finding…

Q: Graph f(x) = x +2x -5 and the tangent line to the graph at the point whose x-coordinate is -2.

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Q: Find where the function f(x) = 3x4 − 4x3 − 12x2 + 5 is increasing and where it is decreasing.…

A: increasing and decreasing intervals of fucntion  fx=3x4 − 4x3 − 12x2 + 5

Q: What is the slope of the graph of f (x) = x3 - 4x2 + 6 at x = 2? Write the equation of the line…

A: Given :        The function f(x) = x3 - 4x2 + 6    To find the slope of the graph f(x) = x3 - 4x2 +…

Q: Find the point of inflection of the graph of the function. f(x) Exvx + 6

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Q: What is an equation of the line that passes through the points (3,4) and (4,6)? Put your answer in…

A: Given             two points P(3,4) and Q(4,6)  To find equation of line passing through these…

Q: Find an equation for the line tangent to f(x)=x3 +3x2 -2x-8, at the point where x=1

A: To find the equation of the tangent line at point x = 1 for the given curve.

Q: Find the derivative of the function: f(x)= 16x5/4 + 8x-1/4 - 7x + 3

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Q: Is the point (-2, 12) on the graph of the function f (x) = x(5 + x)(4 - x)?

A: we have to determine: is the point (-2, 12) on the graph of the function fx=x5+x4-x

Q: What is an equation of the line that passes through the points (0, –5) and (–6,0)? Put your answer…

A: We have to write an equation of the line that passes through the points (0,-5) and (-6,0).

Q: Is the point (1, -2) on the graph of the function k(x) = x2 + (2>x)?

A: Given, k(x) = x2 + (2/x) To check Is the point (1, -2) on the graph of the function

Q: In 1990, tests showed that water in a lake was polluted with 7 milligrams of mercury compounds per…

A: Given, The rate of change in mercury compound per year is drop by 0.75 milligrams per 1000 liters.…

Q: Find the point at which the line f() = --1 intersects the line g(a) 2 + 8

A: Two lines f(x)=-x-1 and g(x)=2x+8 , we have to find the point at which both lines intersects.

Q: The slope of the curev y^2 -xy-3x = 1 at the point (0,-1) is

A: Given curve is: y2-xy-3x=1 ......................... (1) We have to find the slope of this curve at…

Q: Is the point (3, 12) on the graph of the function g(x) = x2 + 5x - 10?

A: Given function, g(x)=x2+5x-10

Q: Find an equation of the line tangent to the graph of f(x) = 1-7x at (-5,- 174).

A: The given function is:fx=1-7x2The coordinate is -5, -174To find equation of tangent line

Q: What is an equation of the line that passes through the points (1,4) and (−2,−8)? Put your answer in…

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Q: Find an equation for the graph sketched below 구 -5 -4 -3 -2 -1 4 5 -4 -5 -- -구 f(x) =

A: Explanation of the answer is as follows

Q: According to an experimental study, the lifespan of a hamster is a function of the time the hamster…

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Q: Find the derivative of 4x +2 -(2) Y = -2x-4

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Q: Find the equation of the curve whose slope is given by 8 1 + x2 and the curve passes through the…

A: Solution

Q: Find the slope of the line tangent to the graph of the function defined by f(x) = 3x2 – 4 at (1,…

A: Solution:Given        f(x)=3x2-4   at (1,-2)To find:Slope of the line tangent to the graph The…

Q: Find the derivative of the function. f(x)=6x3 − 7x2 + 2/x3 − 3

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Q: Find the equation of the secant line on the graph of the function f(x)=7x2 between the points where…

A: take x=-1 . take x=5

Q: Graph f(x) x'- 3x-9x + 2. 3r2

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Q: Find the derivative of the function. 6x - 7x2 + 4 f(x • x³ - 3 f'(x)

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Q: What is the equation of the curve that passes through the point (-2,3) and whose slope function is…

A: In this question, we need to find the equation of curve from the given options.

Q: Find the equation of the linear function whose graph is given here. Use the letter x in your answer…

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Q: is the point (3,-5) on the graph of function f(x)=3/2x-8? yes, no, impossible to determine

A: To decide if the given point lies on the graph: in other words, does the point satisfy the given…

Q: Find the curve whose slope at the point (x, y) is x' +2x² – 7x +9 if the curve is required to pass…

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Q: Find the point on the graph of the function that is closest to the given point. (х) 3 (x - 1)2, (-5,…

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Q: The graph of f is perpendicular to the line whose equation is 3x - 2y - 4 = 0 and has the same…

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Q: f (x) = - 4x² - 6x x²+3

A: The given function is f(x)=4x2-6xx2+3. Find the derivative of the function. Here we use the…

Q: How do I find the equation of the line passing through the pair of points (0,7) and (0,8)?

A: Given points are (0,7) and (0,8).

Q: Find the slope of the line tangent to the graph of f(x) = 3x² - x- 5 at x = 1.

A: The equation of the curve is given by fx = 3x2-x-5 The point is x = 1 Formula Used: mtan = dfdxx=1…

Q: The graph of linear function f passes through the point (1,-9) and has a slope of -3.   What is…

A: Given for a linear function , Slope =-3 and passes through (1,-9)

Q: ntomologists have discovered that a linear relationship exists between the rate of chirping of…

A: Part AWhen the temperature is 60°F, the crickets chirp at the rate of 145 chirps/min, and when the…

Q: The line y - 42-1457 is tangent to the graph of 111 at the point y=2x²-182²-158z+1

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Q: 4. x² + y² = 25 at point (3,4) 2

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Q: Find the equation of the linear function f(x), that has a slope of -2 and passes through the point…

A: Given information: The slope of the equation is -2 and the line passes through the point 5,1.…

Q: Find the points on the graph of the function that are closest to the given point. f(x) = x², (0,8)…

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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.