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How are the graphs #f(x)=absx# and #g(x)=7absx-0.4# related?

Answer 1

Theodore Amidon

g(x)=7f(x)-0.4

If (x, y) is on y=f(x), (#x, 7y-0.4)# is on y = g(x).

For example, #(-1, 1)# is on y = f(x).

#(-1, 7|-1|-0,4)=(-1, 6.6)# will be on y = g(x).

The vertices are (0, 0) and(0, -0.4) respectively.

So, the second makes x-intercepts #+-0.4/7#.

graph{y-|x|=0 [-10, 10, -5, 5]} graph{y-7|x|+0.4=0 [-10, 10, -5, 5]}

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Answer 2

Serenity Jones

The graphs of ( f(x) = |x| ) and ( g(x) = 7|x| - 0.4 ) are related in that they both represent absolute value functions. The graph of ( g(x) ) is a vertical stretch of the graph of ( f(x) ) by a factor of 7 and a vertical translation downward by 0.4 units.

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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.