GRAPHS, TRANSFORMATIONS, AND SOLUTIONS SEC. 3-6 LEQ: WHAT IS THE PROCESS USED TO GRAPH THE OFFSPRING OF PARENT FUNCTIONS?

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Presentation transcript:

GRAPHS, TRANSFORMATIONS, AND SOLUTIONS SEC. 3-6 LEQ: WHAT IS THE PROCESS USED TO GRAPH THE OFFSPRING OF PARENT FUNCTIONS?

GRAPH-TRANSLATION THEOREM

FOR EXAMPLE Solve (y – 2) 2 < 7(y – 2) using the idea of the Graph-Translation Theorem Solutions to the given inequality are 2 larger than solutions to y 2 < 7y. Solve the simpler inequality y 2 – 7y < 0 y(y – 7) < 0 Either (y > 0 and y – 7 0) The solution set to y 2 < 7y is {y: 0 < y < 7} Thus, the solution set to the given inequality is {y: 2 < y < 9}

ANOTHER EXAMPLE Compare the graphs of f and g when f(x) = 2x 5 + 7x + 2 and g(x) = 2(x + 4) 5 + 7(x + 4) – 23. Let y = g(x). Rewrite the formula for g as: y + 25 = 2(x + 4) 5 + 7(x + 4) + 2…added 25 to both sides to make similar to f(x) Since x + 4 has been substituted for x, the graph of g is 4 units to the left of the graph of f Affecting x changes the graph horizontally Always x – h, so x + 4 = x – (-4)…moves negative horizontal direction (left) 4 units Since y = g(x) has been replaced by y + 25, the graph of g is 25 units below the graph of f Affecting y changes the graph vertically Always y – k, so y + 25 = y – (-25)…moves negative vertical direction (down) 25 units

SCALE CHANGES

GRAPH SCALE-CHANGE THEOREM

APPLYING TRANSLATIONS AND SCALE CHANGES TOGETHER

HOMEWORK Pgs #3-11, 14-19