Core Math Investigation

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 = 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 very slow rate of increase for y when x <0.