Given the graph of f(x) = VT as shown, graph the function – 3f(x-1) + 3 %3D 6+ 5- 4+ 2+ 7 6 -5 4 3 -2 -1 234 5 6 -1- -2+ -3+ 4- -5- 3.

Q: Match the function with its graph. f(z) = – 2(x – 3)² 6+ 4 -3 -2 -1 -6 -5 -4-3 -2 -1 -6 -3 -2 3 4 5…

A: The function is given by f(x) = -2x-32

Q: Find the optimal solution for the following function using the graph method? Min Z= 3X1 + 4X2 ST…

A: Given, Min Z=3x1+4x2          subject to X1+X2≤2                            X1+2X2≤5…

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

A: Given

Q: Given a function Ax) and g(x) =-x+1, how would the graph of y = f(x) compare to the graph of y=…

A: Given, a function f(x) and g(x)=-x+1.

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: The graph of y = 5f(x) is obtained by a/an _______stretch of the graph of y = f(x) by multiplying…

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Q: The graph of the function y=-x + 4x is: 12 10 8 6 4 <-12-10 -8 -6 -4 -2 2. 4 10 12 -2 -6 18 10 Find…

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Q: The graph of g(x) = logs(-x) is the graph of f(x) = logsx reflected about the %3D

A: We can plot both the graphs to see thatThe blue curve represents the equation y = log5(x) and the…

Q: Consider the function p(x) = 3x +x - 5x and the graph of y = m(x) below.

A: In the question it is asked to calculate the roots of p(x)=3x3+x2-5x and the graph m(x) given in…

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

A:

Q: Find the x-intercepts of the graph of the function y = – x² – 6x + 3 6土V24 Ox = - 2 6土V48 O x = -2…

A: We have to find the x intercept of given function.

Q: 2. Graph the function: f(x) = - er-1 +2 x y xy

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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…

A:

Q: The graph of g(x) = ax2 opens downward and is narrower than the graph of f(x) = x2  what is value a?

A:

Q: Use the graph of y = f(x) to graph y = f(-x) + 3. (0, 4) (3, 2) (-2, 0) 1- -4-3-2-1, 2 3 4 -2- -3.…

A: Given graph: y=f(x) We need to graph y=f(-x)+3

Q: skecth the graph a) f(x)=(x-2)2(x+3)   b)f(x) = x2-1/x   c)f(x) = 2x/x2-1    d)f(x) = -23 + 7x2 - 2x…

A: To sketch the graph of given function :

Q: (a) Graph f (x) =x+2 for x 0. x+2 for x 0

A: 1.  Graph fx = x+2, for x≤0

Q: The graph of y = f(x) is graphed below. What is the end behavior of f(x)? %3D 60000 50000 40000…

A: We can easily read the end behaviour of the graph by just looking the x values and their…

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: use the graph of y=f(x) to graph g(x)=2f(x-1)+1 given the coordiantes (-4,0) (-2,-2) (0,0) (2,2)…

A: xf(x)-40-2-2002240   let us take x = -3, -1, 1, 3, 5 x   x-1      f(x-1)     g(x) = 2f(x-1)…

Q: Find f^-1 (x), if it exists, and graph both f(x) and f^-1 (x).  f(x)= 2x^3 -3

A: Topic  =Functions

Q: Sketch the graph of the function f. Sx - 3 f(x) 1-2x + 3 if x s 2 if x > 2

A: Given that: f(x)=x-3,      if  x≤2-2x+3,  if x&gt;2

Q: Use the graph of f(x) = lxl to obtain the graph of g(x) = lxl - 4.

A: Given function is fx=x. To transform gx=x-4 from the graph of fx=x. Since the graph of g has -4,…

Q: The graph of the function f(x) =ax2 +bx +c has its vertex at (0,2) and passes through the point…

A: Given that a standard equation of parabola and its vertex and a point that is lie n this parabola.We…

Q: 2. Graph the function: f(x) = S 3x 3x if x < -1 (2x +1 if -1 < x < 3 -2+ -3+ -5+ -6+ -7+ -8+ -9+

A:

Q: The graph of the function f(x) = ax2 + bx + c has vertex at (0, 2) and passes through the point (1,…

A: The graph of the function f(x) = ax2 + bx + c has vertex at (0, 2) and passes through the point (1,…

Q: The graph of the function fCX)=x²+dx+q has only one X-intercept Select a valve for d that satifies…

A: For quadratic equation to be only one x-intercept , discriminant should be equal to zero.

Q: Use the graph of f(x) → 3x² to obtain the graph of h(x) =: 2.

A: Given :      f(x) = 3x2       h(x) = 1/3 x2

Q: Use the graph of a transformed toolkit function to write a formula for the resulting function. y = |…

A: We have to find function using given graph.

Q: Use the graph of y=f(x) to graph the given function. 3+ 2+ -2 -1 y = f(x) 2.

A: Given: y-f(x) To find: y=f(-x)

Q: The graph shows the function y = g(t). 4 3 -1 -1 4 -2 2.

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Q: orm f(x) = ar² + bx +c whose graph %3D

A:

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: The graph f(x)- x² is transformed to create m(x) - f(bx)², where "b" is less than 1 but greater than…

A: Given function is                                                                         f(x)=x2…

Q: The graph of y = f(x) is given. 6- 5 4 3 2 6-5-4-3 -2 -1 -3 -4 -6- 1 2 3 4 5 6 a

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Q: 5 .4 .3 :2 ÷7 -6 –5 -4 -3 –2 -1 1 2 3 4 6 7

A:

Q: b. The graph of f(x) = V is horizontally compressed by a factor of then shifted to the left 3 units…

A: I have appended the concept used in the solution part.

Q: g(x) = −2x + 5 over the restricted domain D = [−3, 2]. Graph.

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Q: Use the graph of y=f(x) to graph the given function. 4 3 2- -3 -2 -1 3 y= f(x) -1- -2- -3- ソ=f(-x) y…

A:

Q: Determine the intercepts of the graph of f(x) = -4x - and 0, 16 (3,0) and 0, and 0, 16 0 and 0, 16 O…

A: Please refer the attached image for complete solution.THANK YOU.

Q: Use the given graph of y = f(x) to solve graph g(x) = f(x - 1) + 1.

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Q: Find the vertex of the graph. f(x) = −x2 + 6x + 1

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Q: The graph of the function f(x)=ax2+bx+c has its vertex at (0, 1) and passes through the point (1,…

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Q: Use the graph of y =f(x) to graph the given function. 4- -5 -2 3 -4 y = -f(x) 3. 2. 1.

A: Consider the figure y=fx, which is given below From the above figure, y=x+3 if −4&lt;x≤−12…

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

A: According to logarithm formula .

Q: Given the graph of f(x) = √x as shown, graph the function - 4f(x − 3). 8+ 7+ 6+ 5+ 4+ 3+ 2+ H -8 -7…

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Q: Based on the graph, find the range of y = f(x). 4. if-6 sx<-2 f(x) = Ixl if -2 sx<8 %3D if 8 sxs 13…

A: Range is those values of y, which has preimage x under given function f(x) that satisfies y=f(x).…

Q: Prove that the graph of the function y = x² −3+1/x has at least two x-intercepts in (0,2).

A:

Q: 4. How are graphs of the functions obtained from the graph of ? (a) y=-f(x)          (b) y =2f(x)-1…

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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.