This document introduces function notation and how to evaluate functions. It explains that f(x) represents the output of the function f for a given input x. Examples show different functions defined using this notation, such as f(x) = 2x + 1. The document also demonstrates how to evaluate functions for given x-values, find x-values for which a function is a certain amount, and graph functions using this notation. It compares translating and shifting graphs of functions.

2. Instead of y = mx +b, we can
write linear functions like this:
f(x) = mx + b
f(x) is read “f of x.”
This means:
The value of function f at x
It does NOT mean “f times x”

3. Can also use other letters
(not just f!)
Examples:
f(x) = 2x + 1
g(x) = -x – 6
h(x) = 4x – 2

4. When we need to evaluate a
function for a given x value, it might
say:
“Find f(3)”
- or -
“Evaluate f(x) when x = 3”
This means:
Find the output when the input is 3.

5. Evaluate f(x) = -4x + 7 when
x = 2.

6. Let g(x) = -x – 1. Find g(4).

7. Let f(x) = 2x – 5.
Evaluate the function when
x = -4, 0, and 3.
f(-4) =
f(0) =
f(3) =

8. For find the
value of x for which h(x) = -7.

9. For find the
value of x so that f(x) = 21.

10. For find the
value of x so that g(x) = -1.

11. To graph in function notation:
Remember: f(x), g(x), h(x) just
replace the y in y = mx + b
(0, b) is still the y-int
m is still the slope

12. Graph f(x) = 2x + 5

13. Graph:

14. Graph each function on the
same graph.
f(x) = 2x
g(x) = 2x + 3
h(x) = 2x – 3
What do you notice about
these 3 graphs?

15. The graph of f(x) + k is a
vertical translation (shift) of
the graph of f(x).
Lines have the same slope but
different y-intercepts.

16. Compare the graph of
g(x) = x – 3 to the graph of
f(x) = x.

17. Compare each graph to the
graph of f(x) = -3x:
g(x) = -3x + 4
h(x) = -3x – 5