The graph shows f(x)=-1/2x+3 and g(x)=-1/2x+3/2. The function g(x) can be written in two different ways as f(x)+k or f(x+h), where h and k are two real numbers. What are the values of h and k? A:k=-3/2 and h=-3 B: k=-3/2 and h=3 C: k=1/2 and h=-3 D: k= 1/2 and h=1/2

Q: Graph the functions ƒ1x2= x1>3 and g1x2= x1>4. Find all points where the two graphs intersect.…

A: The given functions are,

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

A:

Q: Find The value of K, to Continue The function X-2 f(x)= 4-JI4+X メ+23 - %3D メ=2

A:

Q: 5 -6pi 6p -5

A: From the graph, it is clear that the graph is a sine graph because, at x = 0, the sine value is…

Q: The Range of the quadratic function f(x) = -x² + 15x + 45 is O (0,8] О -45, 8 O [-8, 0) O [45, 0) O…

A: By sketching the graph

Q: find the range values of B for which  x2 + 4Bx + B to be positive for all real values of x

A: To find the range values of B for which  x2 + 4Bx + B to be positive for all real values of x

Q: Suppose that f(x) = x2 + 4x - 21.(a) What is the vertex of f?(b) What are the x-intercepts of the…

A: a. The vertex parabola lies at x=-b2a for the f(x) =ax2+bx+c vertex is at x…

Q: Determine the value of f(3) if f(x)=60 (1-e^-0.1t).

A: Given query is to find the value of f(3).

Q: 2. You graph the function f (x)= lx + 21, and your classmate graphs the function g (x)= lx – 21.

A: Given query is to find the similar attributes between f(x) and g(x).

Q: The function f(x) = 2x ^ 3 - 3x ^ 2 - 36x + 2 has its maxima a

A: Introduction :

Q: Find the point of inflection and concave of the graph of the function. (If an answer does not exist,…

A:

Q: Find real values of x for which f(x) = 0. f(x) = 4x + 6

A: To find the real values of x for which fx=0. Solution: Put fx=0 and solve for x.…

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: Find the point at which the line f(x)=-3x+1 intersects the line g(x)=3x+7

A:

Q: The domain of the function f(x)= 50/6x-23 is all real numbers x except for for where x equals?

A: Given

Q: The range of the function f(x) = x2 - 2x + 19 is:

A: In this question we have to find the range of the function given f(x)=x2-2x+19

Q: In a certain lake, the bass feed primarily on minnows, and the minnows feed on plankton. If the size…

A: Given, f (n) = 50 + 2n>150 and g(x) = 4x + 3. we have to evaluate the size of the bass population…

Q: The domain of the function f(x) = V-2x + 58 consists of one or more of the following intervals: (-…

A:

Q: 2) Find the domain of the function. 7- 4x f (x) = 3x + 2

A:

Q: find the value of (k) to continue the function x²-3x2-4x+12 f(x)={ * * 31 x-3 x = 3.

A:

Q: If f (x) =ax³+ bx² , determine a & b so that the graph of f will have a point of inflection at (1,2)

A:

Q: A manufacturer finds that the revenue generated by selling x units of a certain commodity is given…

A: Given: R(x)=80x-0.5x2

Q: Find the x-intercepts of the graph of f(x)= 4x2 + 8x - 3.

A: Given :            f(x) = 4x2 + 8x - 3

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: Determine the points of intersection of the graphs of f(x) = x2 + 5x + 1 and g(x) = - 2x2 - 11x - 4…

A: To find the point of intersection, we need to equate both the functions to each other. Then after…

Q: 2. Find the Domain of the function: h (x) = 4x x (x² – 9)

A: Given function h(x)=4xx(x2-9)

Q: cannot be in the domain of f(x)

A:

Q: 5. Find the value of the function: If f(x) = 3x + 2x 3, find(-3). f(-3) =

A: We have to find the value of the given function at x = -3.

Q: Find the value of c so that the domain of f(x) = √c - x² will be [-5,5].

A: The function f(x)=c-x2 has the domain -5,5

Q: Find the value of x for which the value of the function f(x) = x3 + 3x2 - 2 is minimum?

A:

Q: Find all x-intercepts of the graph of f (x)= x-5x²-36

A:

Q: What are the x-intercepts of the graph of, f

A: f(x) = x2 + 4x -21 When we try to plot it on a X-Y plane, we write y = x2 + 4x -21 When we are asked…

Q: The function ³ - 3x² has a point of inflection at x = 2 x = -2 Ox=0 O x = 1

A: Let the function,   f(x)=x3-3x2

Q: if (gof)(- 1) = 3 and g(x) = 4x 1, find f(-1) :

A: Given that (gof)(-1)=3 and g(x)=4x-1 find f(-1)

Q: If f(x) = ax3 + bx2, determine a and b so that the graph of f will have a point of inflection at…

A: Given f(x) = ax3 + bx2

Q: Find x-intercept(s) of the graph of function g(x)=/3x+7-1.

A: gx=3x+7-1

Q: Determine its vertex and axis of symmetry    f(x) = 3 (x +1)^2 - 6

A:

Q: If g(x) = √100 - x^2 , where - 10 ≤ x ≤ 0, find A) g^-1 (x) B) the domain and range of g^-1

A: g(x)=100-x2y=100-x2x=100-y2x2=100-y2y2=100-x2y=-100-x2 [here 0≤x≤10]g-1(x)=-100-x2 , 0≤x≤10

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: The domain of the function f(x)=22/14x-19 is all real numbers except for ___________

A: Given function f(x) = 22/(14x - 19) Domain of function is all the values where function is well…

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: if f(x)=2x-6 and g(x)=x-x^2 find the value for g(-1)

A: f(x)=2x-6g(x)=x-x2By replacing he value of x with -1

Q: Find the absolute extreme values of the function on the interval.                        g(x) = -x2…

A: given: gx=-x2+11x-305≤x≤6

Q: Suppose f(x) = x² + 3x and g(x) = x. Solve the following inequality using a gn analysis and write…

A:

Q: The function p (x) = x° + x* - x + x2 – x + 5 is graphed on the coordinate plane. As X approaches…

A: graph of the function is shown below

Q: The domain of the function f(x) = V2x + 20 consists of one or more of the following intervals: (- 0,…

A:

Q: The fixed-points of f(x) = (x² + 2) a¹ are 3 and

A:

Q: or what value of X does the function g(x) = 1/3 X3 - 2x2 attain the point of inflexion?

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.