help with precalculus please

Question

1/ Determine whether the graph is the graph of a function.

2/ Determine the intervals on which the function is increasing, decreasing, and constant.

my answer : Increasing on x > - 1; Decreasing on x < - 1

3/ Use the graph of f to estimate the local maximum and local minimum

. 

my answer : Local maximum:  ; local minimum: 

4/ Determine if the function is one-to-one.



Answer 1

Hello, Kacim,

I'm not a mathematician, but here are my comments:

1/ Determine whether the graph is the graph of a function.

1. A function should be continous, This graph shows one function with limits and one constant, again with limits.

2/ Determine the intervals on which the function is increasing, decreasing, and constant.

I see the opposite of what you proposed. The function is increasing for x < -1, and decreasing for x > -1

3/ Use the graph of f to estimate the local maximum and local minimum

I agree with your conclusion, so you'd better check.

4/ Determine if the function is one-to-one.

In order for the function to be one-to-one, it must pass both a the vertical line test AND a horizontal line test.

Vertical line test: draw a vertical line anywhere check whether the line will not intersect the graph more than one time. In other words, the function cannot contain a duplicate x-value.

Horizontal line test: draw a horizontal line anywhere and the line should not intersect the graph more than one time. In other words, the function cannot contain a duplicate y-value.

This graphs fails the horizontal line test, so it is not one-to-one. Is that 1-2-1? Reminds me that 7 8 9, one day, so both 6 and 8 moved.