By J. Newbury PhD (auth.)
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Extra info for Basic Numeracy Skills and Practice
Ili) The behaviour as x becomes very large? The further we go to the right (using positive values of x), the lower the curve drops, but it never reaches the horizontal axis. In a similar fashion, as we move left (using negative values of x) so the graph edges nearer to the horizontal axis from below, and likewise never reaches that axis. (iv) The behaviour as x becomes very small? The smaller x becomes the larger the value of l/x. In fact as x becomes near to 0 we are unable to draw it because the graph becomes too large.
What is its area? Can you evaluate the area as four separate areas? Do you agree that (2x + 1)(x + 2) = 2x 2 + 1x + 4x + 2? Notice that when brackets are elose to each other we intend to indicate a multiplication. Just as xy me ans x x y, so (2x + 1)(x + 2) means (2x + 1) x (x + 2). Exercise 87: Could we simplify the last answer to 2x 2 + 5x + 2? Exercise 88: Expand (2x +1)(3x + 2). If you need to draw a diagram then do so - but can you see how to find the four separate 'areas' without actually drawing anything?
We usually combine these into what is known as the gradient, where, rise gradient = - run: 36 Basic Numeracy Skills Example: If we consider points A and B we get: rise = 5, run · t :. grad len Exercise 124: = 10 = fö5 = "21 Consider points C and B on figure 5. Find the 'rise' and the 'run' and hence the gradient of the line. Notice that the gradients between points C and D, A and B, and C and B are all equal to lh. Since all the points A, B, C and D lie on a straight line then we can say that the gradient of the straight line equals lh.