Given that f(x ) = 4x^3 + 12, evaluate f ( −2) .

In this question we are looking to find a value by substitution. In this case we are substituting the integer (-2) into the equation in place of the x which would be illustrated as f(-2)= 4(-2)^3+12. It is important to place brackets around the -2 as it prevents confusion when multiplying by the power which is the next step. If the substituted value is being multiplied by a power this step is always taken first, so you would first work out (-2)^3 = -8, be careful with the positive and negative signs in the bracket, if the power is an odd number the answer will be negative, if the power is an even number the answer will be positive. We would then adjust our working so that our last previous step is illustrated as f(-2)= 4(-8)+12. You would continue to multiply the brackets out and finally add the 12 so that you are left with a final answer of -20.