Let c be a fixed constant. Explain the relationship betweenthe graphs of: y = f (x + c) and y = f (x) (rectangular).

Q: The equation y =flx) is graphed on the coordinate plane. A function, gx), is the result of…

A: Solve using shifting properties of the graph

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

A:

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: Explain how to graph the reflection of y = f(x) across the x-axis. Give an example.

A: This question comes under the topic of Reflection about the x-axis For getting the reflection of…

Q: (1) Sketch the graph of f(x). Be sure to label the axes and that the graph is consistent with your…

A: We have to graph the given function.

Q: Determine the x-intercept(s) and the y-intercept of the function f : R → R, f (x) = 2x + 5 and…

A: To Determine the x-intercept(s) and the y-intercept of the function f : R → R, f (x) = 2x + 5

Q: 6. Create a graph of the function: y = x(x – 2)²(x + 1) -

A: Graph of functions is given.

Q: If you are given y = f(x), the equation of function f, describe how to find f′(x).

A: If we are given any equation of any function: Here, Given:                        y= f(x) To find…

Q: Consider the function y=f(x). Describe the graph of each transformed function: a) y=-f(x-2)-1 b)…

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Q: f(x) = -(x + 1).

A:

Q: Find the intersection  point of f (y) with x-axis.

A: Given the function f(y) .We need to find the point of intersection of f(y) with x-axis.

Q: Exercise 3: You challenge yourself and graph the given functions on your own 1. y= 2) -3 -2 -1 1. 3.

A: We have to find the graph

Q: Sketch the graph of the curve y=x(x² +2x)², labelling the stationary points and intercepts.

A: Recall: 1) Stationary Point : dydx=0 2) Intercepts :The x-intercept is the point at which the graph…

Q: Sketch the graph of f(x) = Vx - 3 + 4.

A: Given: fx=x-3+4 . Here, the given function is defined only x≥3. The different values of y for x≥3…

Q: Use the graph of y=​f(x) to find each function value.   ​(a) ​ f(−3​) ​(b) ​ f(0​) ​(c)…

A:

Q: Find the function g(x) which is obtained by reflecting the graph of f(x) about y axis and moving 2…

A: solution

Q: The graph of f(x) = where these horizontal tangents occur? 2x+3x – 120x + 20 has two horizontal…

A:

Q: Suppose the cuyahoga river is polluted with 285 parts per million (ppm) of a toxic substance, and…

A:

Q: Explain what is wrong with the following statement: "The graph of f(x, y) = x2 + y? is a circle."…

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.