– 2x – 5 if a < - 3 if -3 < x < 4 Sketch a graph of f(x) = {1 1.5x – 7 if r > 4

Q: (2x+5 if x<-1 6. Sketch (By Hand) a graph of the piecewise defined function: f(x)=- 5-x if x2-1

A: The domain of the first piecewise function f(x) = 2x + 5 is all values of x which are less than…

Q: c. f(1) =3 and lim f(x)=-2 С. x→1

A:

Q: (2x – x? if 0s xS2 2-x if 2<x <3 x-2 if 3<x<4 n if x24 Let f(x) = Sketch a graph of the function in…

A: see below the graph

Q: 2x + 6 if z 2

A: Consider the given function, For the interval x ≤ -3 it is the line f(x) = y = 2x + 6. To draw a…

Q: 52. Let if x 2 | (b) Sketch the graph of g.

A: Domain of g(x) is divided into parts.We have to draw different path for different part of domain.…

Q: Compute all the vertical asymptotes of the function x2 + 1 y = Зх— 2х2 Produce the graph of the…

A: Vertical asymptotes are vertical lines which correspond to the zeroes of the denominator of the…

Q: SKetch graph : f(x) (2-x if xI

A: For  x&lt;-1f(x)=2-xat x=-2   y=f(x)=4at x=-3   y=f(x)=5 Plot this line on graph

Q: Use the graph below to find a 8>0 such that for all x, 0< x-c<6→If(x)- L|<e. 20- /y3x f(x) = x2 c=2…

A:

Q: 4. If f(x) = ax³ + bx², determine a and b so that the graph of f will have a point of inflection at…

A: If fx=ax3+bx2, then to determine a and b so that the graph of f will have a point of inflection at…

Q: Find the domain and asymptote. In interval notation. y=1/x2

A: The given function is,

Q: Find the horizontal asymptote of 2. (x + 3)(5x – 1) y = (5 — г) (5а + 2) f(x)

A:

Q: Find the vertical asymptotes (if any) of the graph of the function.

A: Asymptotes of x2x2-4Vertical asymptotes are vertical lines which correspond to the zeroes of the…

Q: let f(x)= p+ 8/x-q. the line x=4 is a vertical asymptote to the graph of f. what is the value of q…

A: Check point of discontinuity and find q. Then using given intercept point find p.

Q: 7) Sketch a graph for f(x) 3 + 2-x

A: To plot the given function:

Q: S3-x ifxs3 et f(x) = x+3 if x > 3 (a) Evaluate f(-4) and f(3). (-4) = (3) = (b) Sketch the graph of…

A:

Q: -6x - 18 if x -3 fy the general shape and direction of the graph of this function on the interval…

A: We are asked to identify the general shape

Q: 1.5x + 5 if x <- 2 Sketch a graph of f(x) : 6. if -2 <x < 2 -0.5x +7 if x 2

A: Here a function is Given, we have to sketch the graph of the given function. We have to identify the…

Q: Suppose the function f is defined as 6x2-8 over (x-2)(x+4) Write the equation(s) of the vertical…

A:

Q: Find all horizontal and vertical asymptotes. s(x) = 16x2 + 1/4x2 + 10x − 14

A: To find the vertical asymptotes, we determine where this function will be undefined by setting the…

Q: (d) Describe the behavior of the function f (2) around its vertical asymptote at z = -7. f (x) as x…

A:

Q: find all the vertical asymptotes (if any) of the graph of these function f(x)= x2-9 / x3+3x2-x-3…

A:

Q: Find the values of a and b such that (-1, 2) is a point of inflection on the graph of f (x) = ax-…

A:

Q: Which of the following statements about the graph of f(x) = (2.25) shown above are true? Select all…

A: Given graph of f(x)=(2.25)x

Q: Q2// Sketch the graph of the function defined by the formula 0, x 1 |

A:

Q: 2x 4 if x 1 구 6- 5- 4 -8-7 -6 -5 -4 -3 -2 -I 2 5 6 -2 -3 -4- -5 -6- -7- Clear All Draw: 2]

A:

Q: if x 3 Let f(x) = 3-X %3D 2x + 3 (a) Evaluate (-2) and f(3). f(-2) = f(3) = (b) Sketch the graph of…

A:

Q: Find the asymptotes of the functionf(x)=x/x+1.

A: Given function is

Q: Create a function f(x) in standard form with an oblique asymptote at g(x) = - x +4, hole at x = 2, a…

A: Use the following definitions, to obtain the required result. The vertical asymptote occurs when…

Q: 2. Suppose the function f is defined as f(x): vertical asymptote(s) of f.( 6x²-8 (x-2)(x+4)' .Write…

A: As we know that; To calculate the vertical asymptotes, equate the denominator to zero and solve for…

Q: find all asymptotes f(x)=2x/x-1

A:

Q: x3 - 3x2 + 3x + 1 (x) x2 - 3x + 3

A: we have to find

Q: 6. Graph the piecewise defined function. 1x+4] if x2

A: We will make a table for each piece of the function y=|x+4| , x &lt; -3 x -3 -4 -5 -6 y 1 0 1 2…

Q: Q4:- Sketch the following functions showing the detailed steps in different graphs: f) f(x) = 1-x2

A: fx=11-x2

Q: How many asymptotes does the function Ax) = x-1 (x+ 1) have?

A:

Q: (x2 – 6 if x < 1 12x – 5 if x 21' 8) Graph: f(x) Must show your work by creating a table of values.

A: To draw the graph of the given function first we find the function values corresponding to some x…

Q: -x² +1 ifx<0 h(x)={x+1 if 0 <x<1 2 x21 Sketch the graph of h.

A: The given function is as follows.

Q: Which of the following statements about the graph of f (z) (2.25) shown above are true? Select all…

A: We have to find the true Statements regarding the given graph.

Q: 0. if a 2

A:

Q: Use the given graph of function f to solve: Write the equation of the horizontal asymptote, or the…

A: The given graph of the function is:

Q: 13. Use the idea of transfr-mation to sketch the function y = -2f(x+2) + 3 if the graph of y = f(x)…

A: Given: The graph of y=f(x) is

Q: Use the graph of the greatest integer function y =⌊x⌋

A:

Q: 1 if x 2

A: Given the piecewise functionf(x)={1   if x≤-2-x-1  if -2&lt;x≤2-2    if x&gt;2  We need to graph the…

Q: Consider the following function. 4 if x - 3 Step 2 of 3: Identify the general shape and direction…

A:

Q: (-x² +1 if f (x)={ 2x+1 if 01 Sketch the graph of f.

A: To plot the graph first we need to identify the function y = f(x) if the function is parabola, line…

Q: ſ1 – x if xs1 - Let f(x) = |2x + 1 if x> 1 (a) Evaluate f(-2) and f(1). (b) Sketch the graph of f.

A: Given function, fx=1-x     if     x≤12x+1    if     x&gt;1

Q: The graph of f (x)3-x-5x+6 has the point (1, 0) on it. O True O False

A:

Q: 2. Find the value of k if the graph of k f(x) = 3x? has a point of inflection at x = -1.

A:

Q: 18. When is the function, f (x)=: 4 -3x? -3+ below the horizontal asymptote? x-1 5-4x-x2

A: It is given that the function fx=4x-1-3+-3x25-4x-x2. 5-4x-x2=5-5x+x-x2               =51-x+x1-x…

Q: Find the asymptotes of the function f(x)=x3 / x2+1.

A: Since the degree of numerator (3) is greater than the degree of denominator (2), therefore there is…

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.