Function notation
Interpret and apply function notation f(x) in Grade 10 algebra: evaluate f at specific values, find input given output, and compose functions using nested notation like f(g(x)).
Key Concepts
Function notation uses parentheses and letters like $f(x)$ or $g(x)$ to distinguish between equations and clearly state which input to use.
1. Given $f(x) = x + 2$ and $g(x) = x 5$, to find $g(2)$, you use the 'g' equation: $g(2) = 2 5 = 3$. 2. Given $p(x) = x^2 3x$, to find $p( 3)$, you use the 'p' equation: $p( 3) = ( 3)^2 3( 3) = 9 + 9 = 18$. 3. If $a(x) = 9 + 6x$, then $a(2)$ is $9 + 6(2) = 21$.
Function notation is like giving your equations cool nicknames to avoid confusion. Instead of saying 'use the first y equals equation,' you can say 'use $f(x)$'. The value inside the parentheses, like $f(3)$, tells you exactly what number to substitute for $x$. It's a precise and organized way to handle multiple mathematical instructions without mixing them up.
Common Questions
What does f(3) mean in function notation?
f(3) means evaluate the function f at the input x=3. Substitute x=3 into the function rule and compute the output value.
If f(x)=5x-2, find f(-1).
f(-1) = 5(-1)-2 = -5-2 = -7.
If g(x)=x²+1 and g(a)=10, find a.
a²+1=10, so a²=9, a=±3. Both a=3 and a=-3 are valid inputs that produce output 10.