Suppose the graph of f is given. Describe how the graph of y =1-f(-x) can be obtained from the graph of f [Use correct terms: reflect, shift downward, shift upward, etc.]

Q: Sketch the graph of f′. Explain how you found your answer.

A: The given graph is a semicircle with radius 2, so the equation is y=√4-x². The slope of the graph is…

Q: Graph the function f(x) = |x +1+2.

A: Given that  f(x) = |x+1| + 2 Basically , it is a combination of graph  y= x+3  and y=-x+2   As ,…

Q: Graph the function f(x) = -(x- 2) +4.

A: given,         fx=-x-22+4

Q: How can you tell from the graph of a function whetherit is one-to-one?

A: Concept: The calculus helps in understanding the changes between values that are related by a…

Q: Make a rough sketch of a contour map for the function whose graph is shown.

A: The surface of a graph is steep where the level curves are close together and more gradual where…

Q: Use the following graph of f(x) to sketch the graph of f(x-2)-3.

A: The graph of f(x) is given.

Q: Suppose that the graph of a function f is known.  Explain how the graph of of y = f(x) – 2 differs…

A: Let us consider graph of a function y=f(x). Now if we move the graph y=f(x) by c units in downward…

Q: How to tell if a graph represents y as a function of x?

A:

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.