Functions

Let’s say you get a question like this in the exam:

The function f(x)=x³+6x²+13x+2. What is f(2)?

a) 42
b) 60
c) 12
d) 83

This question requires us to understand and apply function notation. A function f(x) represents a relationship between x and y, and an expression like f(2) means f(x) for the value of x=2.

To find f(2), we need to substitute x=2 into the expression x³+6x²+13x+2. This gives us (2)³+6(2)²+13(2)+2, which we then need to simplify to find the value of f(2).

If we begin with the first term (2³), we know that this is equivalent to 2 x 2 x 2 = 23. We can begin with 2 x 2 = 4, and then multiply 4 by 2 one more time to get a result of 8. The next term is 6(2)², so we need to start by squaring 2 to get 4, and then multiply that by 6 to get 24.

After that, the next term is 13(2), which multiply to 26. Finally, we add 2.

Therefore, the equation now reads f(2) = 8 + 24 + 26 + 2.

Our answer is f(2) = 60, which is option (b). To recap:

1. Substitute x = 2 into the equation f(x)
2. Simplify to find the result of f(2)

Example Question/s

Watch video for explanation of the following question/s:

Graph the linear function f(x) = x.

Use the graphs to find the indicated function value.

Example Questions only by Mathematics Vision Project / CC BY-4.0.

Key Rules to remember:

• A function is an equation that has 1 answer for y for every x.

Practice time!

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