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A Function Family Album

A Function Family Album. f(x). Kinds of Functions. Names. Graphs. Linear Constant Identity Quadratic Cubic Exponential And many more!. Straight Line Horizontal Line Slanted Line Parabola Half Parabola Twisted Parabola. How can you tell if it is Linear ?.

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A Function Family Album

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  1. A Function Family Album f(x)

  2. Kinds of Functions Names Graphs • Linear • Constant • Identity • Quadratic • Cubic • Exponential • And many more! • Straight Line • Horizontal Line • Slanted Line • Parabola • Half Parabola • Twisted Parabola

  3. How can you tell if it is Linear? • Graph is a non-vertical straight line • No exponents higher than one • No operations except addition, subtraction, and multiplication • No variables multiplied together • No variables in a denominator • Must be able to put it in the form f(x) = mx + b (where b is a constant and m is a coefficient) The first number is obviously 4

  4. Is it Linear? Why or why not? • f(x) = 4x² + 4 • g(x) = ½ x – 9 • r(x) = √x + 3 • k(x) = kx – 7 • x = 6

  5. Ways to Describe Linear Functions Term Definition • Domain • Range • Y –Intercept • Slope • All Real Numbers • All Real Numbers (unless horizontal line) • Point where line crosses the y- axis • Change in Y/Change in X The second number is obviously 7

  6. Graphing a Linear Function • Example: f(x) = 2x + 4

  7. Two Kinds of Linear Equations Identity Function Constant Function • Parent Function: f(x) = x • Graph: slanted line • Domain: All Real Numbers • Range: All Real Numbers • Y-Intercept: constant • Slope : coefficient of x • Parent Function: f(x) = c • Graph: horizontal line • Domain: All Real Numbers • Range: c • Y-Intercept: c • Slope : zero The third number is obviously 5

  8. Describe the Linear Function • Domain? • Range? • Y-Intercept? • Slope? • Equation? All Real Numbers (-∞, +∞) All Real Numbers (-∞, +∞) 3 3/4 g(x) = ¾ x + 3

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