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How do you find the important points to graph #f(x) = -4x#?

Answer 1

Nathan Axel

It passes through the origin.

#f(0) = 0#

That is the only "important" point that I can think of.

graph{-4x [-10, 10, -5, 5]}

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Answer 2

Ethan Adkins

To graph ( f(x) = -4x ), you can identify the important points using the following steps:

y-intercept: Set ( x = 0 ) and solve for ( y ). In this case, ( f(0) = -4(0) = 0 ), so the y-intercept is at the point ( (0, 0) ).
Slope: The coefficient of ( x ) in the equation ( -4x ) represents the slope of the line. In this case, the slope is -4.
Additional Points: Use the slope to find additional points. For example, if you move one unit to the right from the y-intercept, you move four units down (because the slope is -4). So, from the y-intercept ( (0, 0) ), you get the point ( (1, -4) ).

Plot these points on a coordinate plane and draw a straight line through them to graph ( f(x) = -4x ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.