1. Bell Ringer
If (x) = 3x + 2, then what is the solution of f(2). Hint: substitute 2 in for x.
2) If f(x) = 2x2 – 3x + 4, then what is f(3), or what’s the solution when you substitute 3 in for x?

2. f(x) = mx + b Function Notation-
Linear Functions
Function Notation-
a linear function written in the form y = mx + b where y is written as a function f.
x-coordinate
f(x) = mx + b
This is read
as ‘f of x’
slope
y-intercept
f(x) is another name for y.
It means “the value of f at x.”
g(x) or h(x) can also be used to name functions

3. Domain and Range
Domain = values of ‘x’ for which the function is defined.
Range = the values of f(x) where ‘x’ is in the domain of the function f.
The graph of a function f is the set of all points (x, f(x)).

4. Graphing a Function To graph a function:
(1) make a table by substituting into the function.
(2) plot the points from your table and connect the points with a line.
(3) identify the domain and range, (if restricted)

5. Graph the Function f(x) = 2x – 3
Graph a Function
Graph the Function f(x) = 2x – 3
SOLUTION
STEP 2
STEP 3
STEP 1
Plot the points. Notice the points appear on a line. Connect the points drawing a line through them.
The domain and range are not restricted therefore, you do not have to identify.
Make a table by choosing a few values for x and then finding values for y. x -2 -1 1 2
f(x) -7 -5 -3

6. Graph a Function 1 2 Graph the function f(x) = – x + 4
with domain x ≥ 0.
Then identify the range of the function.
STEP 1 x 2 4 6 8 y 3 1
Make a table.
STEP 2
Plot the points.
Connect the points with a ray
because the domain is restricted.
STEP 3
Identify the range. From the graph, you can see that all points have a y-coordinate of 4 or less, so the range of the function is y ≤ 4.

7. Family of Functions
is a group of functions with similar characteristics. For example, functions that have the form f(x) = mx + b constitutes the family of linear functions.

8. Parent Linear Function
The most basic linear function in the family of all linear functions is called the PARENT LINEAR FUNCTION which is:
f(x) = x
f(x) = x x -5 -2 1 3
f(x)

9. Real-Life Functions
A cable company charges new customers $40 for installation and $60 per month for its service. The cost to the customer is given by the function f(x) = 60x +40 where x is the number of months of service. To attract new customers, the cable company reduces the installation fee to $5. A function for the cost with the reduced installation fee is g(x) = 60x + 5. Graph both functions. How is the graph of g related to the graph of f ?

10. Real-Life Functions
The graphs of both functions are shown. Both functions have a slope of 60, so they are parallel. The y-intercept of the graph of g is 35 less than the graph of f. So, the graph of g is a vertical translation of the graph of f.

11. Write an Equation Given a Slope and a Point

12. Write the Equation using Point-Slope Form
Step 1: Plug it in
Point- Slope Form

13. A Challenge
Write the equation of a line in point-slope form that passes through (-3,6) and (1,-2)
Hint: Find the change in y and the change in x.
Change is determined by subtraction.
Reminder that slope is rise or run.

14. A Challenge
Can you write the equation of a line in point-slope form that passes through (-3,6) and (1,-2) 8 2
6 + 2
-3 – 1
= - 4 1
Calculate the slope.
m =
y – y1 = m(x – x1)
Use m = and the point (1, -2).
y + 2 = - 2 (x – 1)
Point-Slope Form
y = -2(x – 1) - 2
y = -2x
Slope-Intercept Form
y = -2x + 0
y = -2x

15. Equations of Parallel Lines
Write an equation for the line that contains (5, 1) and is parallel to
m =

16. Equations of Perpendicular Lines
Find the equation of the line that contains
(0, -2) and is perpendicular to y = 5x + 3
m =