About Function Notation:
When we work with functions, we have a 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 function's 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
#1:
Instructions: for the given function, find f(1), f(9), and f(2).
a) 
Instructions: for the given function, find f(-3), f(1), and f(5).
b) 
Watch the Step by Step Video Solution View the Written Solution
#2:
Instructions: for the given function, find f(-2) and f(2).
$$a)\hspace{.2em}f(x)=x^2 - 3x - 5$$
Instructions: for the given function, find f(1) and f(6).
$$b)\hspace{.2em}f(x)=\frac{1}{x^2 - 5x - 6}$$
Watch the Step by Step Video Solution View the Written Solution
#3:
Instructions: for the given function, find f(10) and f(-2).
$$a)\hspace{.2em}f(x)=\sqrt{3x + 6}$$
Instructions: for the given function, find f(a) and f(a + 1).
$$b)\hspace{.2em}f(x)=x^2 - 2x - 1$$
Watch the Step by Step Video Solution View the Written Solution
#4:
Instructions: for the given function, find f(z - 1) and f(z2).
$$a)\hspace{.2em}f(x)=x^3 + 2$$
Instructions: for the given function, find f(q - 3) and f(q3).
$$b)\hspace{.2em}f(x)=\sqrt[3]{x}+ 7$$
Watch the Step by Step Video Solution View the Written Solution
#5:
Instructions: for the given function, find f(-7) and f(3).
$$a)\hspace{.2em}3x - 5y=20$$
Instructions: for the given function, find f(z + 1) and f(z - 2).
$$b)\hspace{.2em}9x^2 - 3y=27$$
Watch the Step by Step Video Solution View the Written Solution
Written Solutions:
#1:
Solutions:
$$a)\hspace{.2em}f(1)=3, f(9)=19, f(2)=-4$$
$$b)\hspace{.2em}f(-3)=3, f(1)=-1, f(5)=3$$
Watch the Step by Step Video Solution
#2:
Solutions:
$$a)\hspace{.2em}f(-2)=5, f(2)=-7$$
$$b)\hspace{.2em}f(1)=-\frac{1}{10}, f(6) \hspace{.2em}\text{is undefined}$$
Watch the Step by Step Video Solution
#3:
Solutions:
$$a)\hspace{.2em}f(10)=6, f(-2)=0$$
$$b)\hspace{.2em}f(a)=a^2 - 2a - 1 $$ $$f(a + 1)=a^2 - 2$$
Watch the Step by Step Video Solution
#4:
Solutions:
$$a)\hspace{.2em}f(z - 1)=z^3 - 3z^2 + 3z + 1$$ $$f(z^2)=z^6 + 2$$
$$b)\hspace{.2em}f(q - 3)=\sqrt[3]{q - 3}+ 7$$ $$f(q^3)=q + 7$$
Watch the Step by Step Video Solution
#5:
Solutions:
$$a)\hspace{.2em}f(-7)=-\frac{41}{5}$$ $$f(3)=-\frac{11}{5}$$
$$b)\hspace{.2em}f(z + 1)=3z^2 + 6z - 6$$ $$f(z - 2)=3z^2 - 12z + 3$$
