Use the graph of f(x) = 3√ x to obtain the graph of g(x) = -3√x.

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  &  gx=3x+a Now, f∘gx=fgx=f3x+a=23x+a2+5

Q: how is the graph g(x)=(x-6)^2-4 related to the graph of f(x)=x^2?

A: In this question transfomation takes place.

Q: g(x) = V8x – 1

A: We need to find the range (y-axis)

Q: How is the graph of g(x) = (x - 8) 2 + 7 transformed from the graph of f(x)=x2?

A: g(x) = (x - 8)2 + 7 f(x) = x2 is the parent function. The function g(x) can be obtained by applying…

Q: Use the graph of f(x) = 2x to obtain the graph of g(x) = 2x - 3.

A: Given

Q: How Is the graph of g (x)=x2+14 related to the graph of f(x)=x2? The graph of g (x)=x²+14Is the…

A:

Q: For Exercise, refer to c(x) = x3 – 4x2 – 2x + 8 and d(x) = x3 + 3x2 – 4. c(x) - 4x2 – 2x + 8 Find…

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Q: I. Sketch the graph of the following 1. f(x) = 22r-1 2. g(x) = A

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Q: Explain how the graph of f(x) = 2Vx – I + 3 is related to the graph of y = Vx.

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Q: neath the graph of f(x) = 7x³ about the y-axis ov

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Q: Q3/ Sketch the graph of f(x) = x+1

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Q: snip

A: We have given f(x)=2x2+5, g(x)=3x+a and f∘g crosses the y-axis at 23. f∘g (read as "f of g") is a…

Q: For f(x) = find the x² + 3x + 2 domain, VA, HA and both x and y intercepts to graph. 3.

A:

Q: D) The x-intercept of the graph of f is -4.

A: Given that: The two points ( - 4, 0 ) and ( 2, - 8 ).

Q: 8. f(x)=1+2Vx+4

A:

Q: e) Draw the graph of f. x2 f(x) 16 — х2

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Q: Given the graph of f (x) below and g(x) = 3x + 7 %3D which is the distance between the two y-…

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Q: For f(x) = x^3 + 5, write the rule for g(x) = f(x - 1) – 2 and sketch its graph

A: The function is given by f(x) = x3+5 To evaluate : The rule for g(x) = fx-1-2 and sketch it.

Q: For Exercise, graph the equation. Slx| + 1 for x 1 уз

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Q: Let f(x) = -0.4x² + 6x-12. Find the x-coordinate of the vertex. Round your answer to 2 decimal…

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Q: We are given f(x) = 9x2 and f '(x) = 18x. Find the point on the graph of  y = f(x) at x = 2.

A: Given:

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: The graph of f(x) = x³ + 6x² + 7x has a point of inflection at r = -5 -2 1 -1 O 3

A: Consider the following function: fx=x3+6x2+7x Differentiate fx with respect to x:…

Q: 61. If f(x) = 2x² + 5 and g(x) = 3x + a, find a so that the graph of fo g crosses the y-axis at 23.

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

Q: Suppose the point (b, 0) is on the graph of f(x) = 8x – 16, then the value of b is Answer:

A:

Q: Use the graph of f(x) = |x| to graph g(x) = – |2x|.

A: To obtain the graph of y=-|2x| from that of y'|x| by using a sequence of transformations

Q: r f(x)=x^2/(1+x), determine the concavity of the graph o

A:

Q: The graph of f(x) = x2_______ to the left and_______ to the right.

A: The graph of f(x) = x2_______ to the left and_______ to the right.

Q: Find the domain and sketch the graph of the function. f(x) =2t+t2

A: Given: fx=2x+x2 we know that given function is a quadratic function whose constant term is zero we…

Q: . The x-coordinate of the vertex of f(x) = ax2 + bx + c,a ≠ 0, is_________

A:

Q: (a) How is the graph of y = f(x – 3) + 2 obtained from the graph of f? (b) How is the graph of y =…

A: Let the given graph is f(x). (a) To obtain the graph of y=f(x-3)+2 First, horizontally translate the…

Q: Given g(x) = 3x + 3, find four points on the graph of the function.

A: gx = 3x+3four points on the graph of g(x) = ?3x+3 ≥ 03x ≥ -33x3≥- 33x ≥ -1So the domain is [-1, ∞).…

Q: Explain how the graph of f(x) = mx + b can be used to solve mx + b > 0.

A: f(x)=mx+ b

Q: Use the graph of y = f(x) given above to find: a) f(-1) = b) f(-3) =

A: We have to find the following values using the given graph.

Q: If f(x) = 3x^2 − 7 and g(x) = 2x + a, find a so that the graph off ◦ g crosses the y-axis at 68.

A: Given

Q: . Given f(x)=-x²+4x+12, 05x58: (a) Carefully, graph f(x), 0sxs8.

A:

Q: Use the graph of f(x) = 2x² – 5v2x + 3 to sketch the graph of f (x) – 3.

A: It is given that the function fx=2x2-52x+3. We have to use the graph of the function fx to sketch…

Q: The x-coordinate of the vertex of f(x) = ax2 + bx + c, a ≠ 0, is ________.

A: For the standard form of a parabola:  fx=ax2+bx+c If a>0, the parabola opens up and the vertex…

Q: On what interval is f(x) = x³ + 3x² – 24x +7 decreasing? The graph is decreasing on the interval

A: Use first order derivative test to obtain the interval of decrease.…

Q: Match the function with its graph. f(x) = x2 + 6x + 8

A: In the question we have to find graph of the function.

Q: Next, use the vertex and the other point provided to find the value of the leading coefficient a in…

A: Given that vertex is at -3,5, thus, h,k=-3,5.

Q: 30) Use the graph to: a) Identify where f(x) is undefined or b Solve(

A: a) From the given graph, observe that the graph of the function y = f (x) is undefined at the point…

Q: If g(x) = x2 – 4, where does the graph of the g(x) cross the x-axis? Make a sketch of the graph.

A: Given g(x)=x2-4We know that x2 graph is a prabola

Q: Sketch the graph of the following fu f(x) = (x + 3)4 he correct graph below OC.

A:

Q: how is the graph of g(x)=x³+2 related to the graph of f(x)=x^3

A: The graph of  x3 and x3+2 are related to each other.  Both the graphs work in same sense but graph…

Q: The graphs of f (x) = 2" and g(x) = 3"- are shown. %3D

A: According to logarithm formula .

Q: Sketch the graph of f.

A: Given that

Q: Is the graph of g(x)=4x^3+9x^2+7x+3 concave up or down at the point with x-coordinate −2?

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.