Solving functions out from a graph - finding the image of a function - curve intervals

Question

The question states: "The image below shows the curve of the function f(x) where Df = [-2,2]. Use the graph to answer the following questions: (I have linked said image)

a) find the image of function f

b) solve the equation f(x) = 0

(Here I would assume y = 0, given the graph)

c) solve the equation f'(x) = 0

d) solve the equation f''(x) = 0

e) at what interval does the function curve downward?

Here is the graph attached:

https://ibb.co/yXTX407

Again any help would be appreicated.

Answer 1

This question may have got lost in translation. I the link to the graph isn't clear for me. However to aid in solving this type of problem I can assume we are working with the domain restriction of [-2,2] so only assess the graph in that range.

b) yes set y=0 This would imply that in part a) you found the equation to the graph.

c) you will use the derivative of the function and set that =0. The derivative of the function tells us where the function is increasing and decreasing. Using a line plot we can check above and below the zeros for a negative or positive answer. Positive tells us that part of the graph is increasing while negative tells you it is decreasing.

d) Find the derivative of the derivative. This is a double derivative. Derive the first derivative to find the second. Set that equal to zero and solve. The answers here show inflection, where the graph changes concavity. Again you will use a line plot checking each side of the zeros for positive or negative.

e) The domain section that is negative is where the function curves downward.

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