4.05: Graphing Exponential Functions Essential Questions 4.05 How can graphs be created from verbal expressions? · How can the key features of an exponential function be compared through tables · and graphs? What effect will introducing a constant have on an exponential function? · Note-taking Guide: Main Idea DEFINITION OR SUMMARY EXAMPLE (page #) A function that increases by a factor, moving from left to right on the x-axis; the base of the exponential expression in this function must be greater than 1. Exponential f(x) = 1000(0.95)^x; Decay (pg 2) examples will vary but need (less than 1)^x Can be found by making x=0 f(x)=a(b)^0 Vertical Shifts f(x)+k= P(1+r)^x + k Example: f(x) +6 = (pg 5) If k is positive, the graph shifts ________. 2(3)^x + 6 If k is negative, the graph shifts ________. Horizontal f(x + h) = P(1 + r)x Example: f(x + 6) = + h Shifts(pg 5) If h is positive, the graph shifts ________. 5(4)x +6 If h is negative, the graph shifts ________. Negative If the exponent switches signs, it reflects the Exponents graph over the _____________________, but the (pg 6) y-intercept stays the same.
4.05: Graphing Exponential Functions Essential Questions 4.05 · How can graphs be created from verbal expressions? · How can the key features of an exponential function be compared through tables and graphs? · What effect will introducing a constant have on an exponential function? Note-taking Guide: Main Idea (page #) DEFINITION OR SUMMARY EXAMPLE A function that increases by a factor, moving from left to right on the x-axis; the base of the exponential expression in this function must be greater than 1. Exponential Decay (pg 2) f(x) = 1000(0.95)^x; examples will vary but need (less than 1)^x Can be found by making x=0 f(x)=a(b)^0 Vertical Shifts (pg 5) f(x)+k= P(1+r)^x + k If k is positive, the graph shifts ________. If k is negative, the graph shifts ________. Example: f(x) +6 = 2(3)^x + 6 Horizontal Shifts(pg 5) f(x + h) = P(1 + r)x + h If h is positive, the graph shifts ________. If h is negative, the graph shifts ________. Example: f(x + 6) = 5(4)x +6 Negative Exponents (pg 6) If the exponent switches signs, it reflects the graph over the _____________________, but the y-intercept stays the same.