# Problems from Functions: Graphic representation

Considering the functions

1) $$f(x) = 3x - 4$$

2) $$g (x) = -x^2-2x$$

do a values table for each of them which enable their subsequent representation.

See development and solution

### Development:

1) $$f(x) = 3x - 4$$

Being a straight line, having two points would be enough to represent it. Nevertheless, we will always look for three, since this way we can detect errors (when three non aligned points come out).

 $$x$$ $$f(x)$$ $$0$$ $$-4$$ $$1$$ $$-1$$ $$2$$ $$2$$

2) $$g(x)= -x^2-2x$$

Initially we notice that the function is a parabola that is opened downwards (it presents a maximum).

Let's look for the coordinates of the vertex:

$$v=\Big( \dfrac{-b}{2a}, -\dfrac{b^2-4ac}{4a} \Big) = (-1,1)$$

We can also give three or four values neighboring the vertex to help in the representation:

 $$x$$ $$f(x)$$ $$-3$$ $$-3$$ $$-2$$ $$0$$ $$0$$ $$0$$ $$1$$ $$-3$$

### Solution:

This way, we have obtained the following values that will allow us to represent the function:

1)

 $$x$$ $$f(x)$$ $$0$$ $$-4$$ $$1$$ $$-1$$ $$2$$ $$2$$

2)

 $$x$$ $$f(x)$$ $$-3$$ $$-3$$ $$-2$$ $$0$$ $$0$$ $$0$$ $$1$$ $$-3$$
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