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Bell Ringer

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

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Bell Ringer

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  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. 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 a Function Graph the Function f(x) = 2x – 3 SOLUTION STEP2 STEP3 STEP1 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.

  6. – x+ 4 Graph the functionf(x)= with domainx ≥0. Then identify the range of the function. 1 2 Graph a Function STEP1 Make a table. STEP 2 Plot the points. Connect the points with a ray because the domain is restricted. STEP3 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

  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) m = Calculate the slope. 6 + 2 8 2 = - = - -3 – 1 4 1 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

  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 =

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