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Identify BOTH exponential functions y = 2x3 y = 3x2 y = 3 • 2x y = 2 • 3x Yes, Exponential NO WAY !!! y = 7 • 5x ? y = 0 • 5x ? Yes, Exponential NO WAY !!! y = 9•(4)x ? y = 9•(-4)x ? Yes, Exponential NO WAY !!! y = 3 • 5x ? y = 3 • 1x ? Is NOT an exponential function. Multiplying by 1 repeatedly does not CHANGE (grow or decay) the initial value. y = 3 • 1x Other exponential functions: A function such as y=2 is an exponential function. x y = 3 y = (4.2) y = (½) x x x A function such as y=2 is an exponential function. Which is NOT an exponential function: Exponential Function y = 3x y = (4.2) y = (¾) x x x y = 3x is NOT an exponential function. It is a linear function. A function such as y=2 is an exponential function. y = 3x x Thanksgiving -style, Set a Table But Mr.! How do I graph Exponential Functions?!!! x 0 1 2 3 x Drag in x values so you can find 3 3 3 3 0 ? 1 ? 2 ? x Hint: Any # raised to the zero power equals 1 x 0 1 2 3 1 ? 9 ? 3 ? x 3 3 3 0 1 2 Drag the correct values in the table x 0 1 2 3 1 3 9 x This is an exponential function graph x 0 1 2 2 1 ? 4 ? 2 ? x Is an exponential function fill in the x values to make a new power of 2. y = 2 x 2 -2 4 -4 2 -2 4 -4 6 -6 . . . . . x . 0 1 2 . 2 1 2 4 . x . . . . . Click a dot to plot (0,1) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 -2 4 -4 2 -2 4 -4 6 -6 . . . . . x . 0 1 2 . 2 1 2 4 . x . . . . . Click a dot to plot (1,2) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 -2 4 -4 2 -2 4 -4 6 -6 . . . . . x . 0 1 2 . 2 1 2 4 . x . . . . . Click a dot to plot (2,4) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 -2 4 -4 2 -2 4 -4 6 -6 . . . . . x . 0 1 2 . 2 1 2 4 . x . . . . Exponential graphs are curved . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x 3 4 5 6 2 x-3 Fill in the table blanks 2 2 3 -3 4 -3 = = 2 2 0 1 = = ??? x 3 4 5 6 2 1 2 x-3 Fill in the table blanks 2 2 5 -3 6 -3 = = 2 2 2 3 = = ??? x 3 4 5 6 2 1 4 8 2 x-3 2 Completed table. 2 5 -3 6 -3 = = 2 2 2 3 Which is the graph of an exponential function? Blue graph Red graph Green graph x 0 1 2 3 (½) ½ ? ¼ ? ⅛ ? 1 ? x (½) (½) (½) (½) 0 1 2 3 = = = (½) (½) (½) * * (½) (½) * (½) x 0 1 2 3 (½) 1 ½ ¼ ⅛ x (½) (½) (½) (½) 0 1 2 3 = = = (½) (½) (½) * * (½) (½) * (½) Look at the graph for y = (½) When x = 0, y = 1 x When x = -1 y = Look at the graph for y = (½) x When x = -1 y = 2 Look at the graph for y = (½) x When x = -2, y = Look at the graph for y = (½) x When x = -2, y = 4 Look at the graph for y = (½) x Done & Done |