The graph of y = f(x) has x-intercepts of -2 and 7, and a y-intercept of 4. Find the axes intercepts of: (a) g(x) = f(x)– 2. (b) h(x) = f(x+1). (c) j(x)=-2f(x).

Q: Find the equation of a line which has y-interept 4,and is parallel to the line 2x-3y-7=0 ,Find the…

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Q: Graph of the equation f(x) = 3x - 3 in the xy-Coordinate Plane.

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Q: For Exercise, estimate the x- and y-intercepts from the graph. 3-2 –1

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Q: b. Find the slope of the curve at the given point. y* = 2x; (648,6)

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Q: Find the relative maximum point of the curve: Y=16x+4x2-x4

A: Solution of question as follows

Q: Find the relative maximum and minimum values. =x2 + y² - 6x + 12y - 9

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Q: Find a general form of an equation of the line through the point A that satisfies the given…

A: Given that line passes through point A and having x-intercepts = 4 and y-intercepts = -3

Q: Find the equation of a line which has y-intercept 4,and is parallel to the line 2x3y-7=0,Find the…

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Q: Sketch the graph of 3x - 2y = 12 using the slope-intercept method:

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Q: Find the point at which the line f(x) = - 2x +4 intersects the line g(a) = -a

A: Given, f(x)=-2x+4 and g(x)=-x

Q: Find the slope of the curve y = x3 + 8x +14, where the curve crosses the x-axis

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Q: 2. Trace the curve x3 – 6x² + 11x – y = 6. -

A: Given curve is, x3-6x2+11x-y=6 That is, y=x3-6x2+11x-6 1) Domain and Range of given curve:    This…

Q: Q11. Obtain the general equation of the curve whose slope at any point is equal to y - 2x.

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Q: Find the x-intercept and the y-inercept x-3y=-3

A: The y-intercept of the function is computed as follows.

Q: 1) Find the equation of the curve whose slope at any point p(x,y) is m = (x * +16x + 4)²(x ³ + 4)…

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Q: Approximate the solution(s) to x3-2x+2=0 using a graphing utility

A: x3-2x+2=0

Q: Find the x and y intercept(s) of y=x2+4x+3

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Q: Determine the equation of the vertical trace of the function g(x,y)=-x^2-y^2+2x+4y-1 corresponding…

A: To find equation of vertical trace we need to substitute value of variable in the given equation of…

Q: Find the point at which the line f(x) intersects the line g(x) = 2x + 5 = – 2x + 1 -

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Q: Determine the slope of the graph of 3(x2 + y2)2 = 100xy at the point (3, 1).

A: Given: 3x2+y22=100xy we know that slopem at given pointx1,y1 is given by m=dydx|x1,y1 so, we…

Q: Find the point on the line -4x + 7y + 1 = 0 which is closest to the point (– 1, 3). %3D

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Q: The pollution level in the center of a city at 4am is 22 parts per million and it grows in linear…

A: (A) The pollution level in the center of a city at 4am is 22 parts per million. It grows in linear…

Q: Find the standard form for the equation of the line which passes through the point (2,0) and which…

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Q: Find the y-intercept. (x+1)(x-5) g(x)= (x+3)(x-3)

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Q: Find the equation of the line perpendicular to 8x + 2y = 1 passing through the point (4, Y = -X

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Q: A3) Find the equation of the line tangent to the graph of f(x) = 5x3 + 8x² – 2x – 3 at x = -7.

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Q: Find the equation of line (L) that passes through the intersection point of the two functions y = v2…

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Q: At x = 2, the slope of the curve y = 2x3

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Q: Find the slope of the curve y = 2x* + 3x³ + 2x2 – 1 at a point where it crosses the x-axis

A: y=2x4+3x3+2x2-1 A curve crosses the x-axis at a point where its y-coordinate is zero. Therefore…

Q: Explain the steps to find x- and y- intercepts of an equation of the form Ax + By = C

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Q: Find the slope of the curve given by f(x)=x3e4x at the point (-1,-e-4)

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Q: Graphically, find the point (x1, y1) which lies on both lines 2x + y = 4 and x −y = 2.

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Q: f(x) = 2 x-6x-7 8-2

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Q: A market analyst working for a small appliance manufacturer finds that if the firm produces and…

A: we are given with profit equation  Lets graph the given equation  the x intercepts are (-45.224,0)…

Q: The graph of linear equation x+2y = 2, cuts the y-axis at:

A: Given linear equation is x+2y=2.

Q: Find the x- and y-intercepts of the graph of the equation. (If an answer does not exist, enter DNE.)…

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Q: A geologist measures the temperature T (in C) of the soil at various depths below the surface and…

A: Givent that a geologist measures the temperature T in celcius of the soil at various depths below…

Q: Find the point at which the line f(x)=−5x−3f(x)=-5x-3 intersects the line g(x)=−x+1g(x)=-x+1

A: The given functions are fx=-5x-3gx=-x+1

Q: The line shown above has an y-intercept of T

A: From the graph we can see that the line intersect the y-axis at y = 1

Q: The graph of y = x3 + ax2 + bx + 7 has an inflection point at (2,-10). Find the value of a and b.

A: Given that the graph of y=x3+ax2+bx+7 has an inflection point at (2,-10).we have to find the values…

Q: Find the equation of line (L) that passes through the intersection point of the two functions y = v2…

A: Given functions: y=2-x2y-2x+3=0 Equation of perpendicular line is, 2x-4y=6

Q: The graph of y = x3 + ax2 + bx + 7 has an inflection point at (2, -10). Find the value of a and b.

A: we have been given that the graph of y=x3+ax2+bx+7 has an inflection point at (2,-10). we have to…

Q: Approximate the solution(s) to x3 - 2x + 2 = 0 using a graphing utility.

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Q: Find the equation of the line parallel to the line y= 4x+3 and passes through the point (0,2)

A: This question is based on equation of line.

Q: Find the curve whose slope at any point (x,y) is 6x^2−2x−5 if the curve is required to pass through…

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Q: Find the slope of x²y=8 at the point (2,2).

A: Given: x2y=8 To find: Slope of x2y=8 at (2,2)

Q: Which of the following is the y-coordinate for the point that lies on the line y=-3/4x+1 and has an…

A: substitute the  value of x .

Q: Find the x- and y-intercepts of the graph of the equation. x2 - xy + y = 1

A: We need to find the x- and y-intercepts of the graph of the equation x2 - xy + y=1. To find the…

Q: 2) Find an equation for the slope of the graph of y=x²+2x at any point.

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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.