# Core Math Investigation

Essay by MapleLink August 2014

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Core Math Investigation 1) When x is more than 0 and increases (e.g. from 5 to 6), y increases at a much faster rate and becomes very big. When x increases when it is less then 0 (e.g. from -10 to -9), y increases very slowly. 2) (i) The value of a affects the value of x proportionally. For example we can compare the equations y = 1 + 2x and y = 5 + 2x. In the second equation, the value of a has been change to 5. As we can see from the results in Tables 1 and 2, all the values of y for y = 5 + 2x are greater by 4, when x is the same. (ii) As we have seen in (i), the effect of a does not affect the value of y, as it is a constant added to the solution of 2x . Hence, the value of a affects x proportionally, no matter what the value of x is.

3) (i) For b = -1, b causes the value of y decrease rapidly as x increases. This is because when x becomes larger, bx will be a very small number as bx will be small as b is negative while x is positive. For b = 0, y remains constant throughout, no matter what the value of x is. This is because 0x will always give 0. For b = 1, the relationship is the same as in (1), as 1x will always lead to a rapid rate of increase for y when x> 0. (ii) For b = -1, b causes y to increase greatly when x gets smaller, as b is a negative number and so bx will give a large number when both b and x are negative. For b...