About Function Notation:

When we work with functions, we have specific notation that applies. Generally instead of y, we will now see f(x), g(x), or h(x). When we have a function, we can use the notation to ask for the functions value, given a certain input. If we see f(2), this means replace the independent variable with 2 and evaluate.


Test Objectives
  • Demonstrate the ability to write a function using function notation
  • Demonstrate an understanding of f(a), where a is a real number
  • Demonstrate an understanding of f(x + a), where a is a real number
Function Notation Practice Test:

#1:

Instructions: Find f(0), f(-1), and f(-5).

a) $$f(x) = 7x^2 - x + 5$$


#2:

Instructions: Find f(-2), f(6), and f(12).

a) $$f(x) = -\frac{1}{4}x + 3$$


#3:

Instructions: Find f(c), f(c + 3), and f(c - 1).

a) $$f(x) = -x^2 + 5x - 9$$


#4:

Instructions: Find f(-2), and f(z-3).

a) $$-9x + 3y = -24$$


#5:

Instructions: Find f(-3), and f(b + 4)

a) $$2x^2 + 4y = -12$$


Written Solutions:

#1:

Solutions:

a) $$f(0) = 5$$ $$f(-1) = 13$$ $$f(-5) = 185$$


#2:

Solutions:

a) $$f(-2) = \frac{7}{2}$$ $$f(6) = \frac{3}{2}$$ $$f(12) = 0$$


#3:

Solutions:

a) $$f(c) = -c^2 + 5c - 9$$ $$f(c + 3) = -c^2 - c - 3$$ $$f(c - 1) = -c^2 + 7c - 15$$


#4:

Solutions:

a) $$f(-2) = -14$$ $$f(z-3) = 3z - 17$$


#5:

Solutions:

a) $$f(-3) = -\frac{15}{2}$$ $$f(b + 4) = -\frac{b^2}{2} - 4b - 11$$