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?

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

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)).

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)

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

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.

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.

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)

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 ?

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.

Write an Equation Given a Slope and a Point

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

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.

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 = - 2 and the point (1, -2). y + 2 = - 2 (x – 1) Point-Slope Form y = -2(x – 1) - 2 y = -2x + 2 - 2 Slope-Intercept Form y = -2x + 0 y = -2x

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

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