MATH 1310 Section 5.1

The Exponential Function An exponential function is defined as a function of the form: f(x) = ax where a > 0. This is considered an exponential function with base a.

f(x) = c ax (1,6) and (2, 12)

Popper 27: Consider the function: f(x) = 4 (2/3)x-1 + 5 What is this function called? Quadratic b. Rational c. Exponential d. Polynomial 2. Is this function increasing or decreasing? Increasing b. Decreasing c. Cannot be determined 3. What is the horizontal asymptote of the function? a. y = 5 b. y = 4 c. y = 2/3 d. None

Popper 27…continued: Consider the function: f(x) = 4 (2/3)x-1 + 5 4. What is the domain of the function? (-∞, ∞) b. (5, ∞) c. [5, ∞) d. (4, ∞) 5. What is the range of the function? 6. Which of the following points does the function pass through? a. (0, 1) b. (0, 5) c. (0, 4) d. (0, 11) 7. Which transformations are present? a. Horizontal Shift b. Vertical Shift c. Vertical Stretch d. All of above

Sketch the graph: f(x) = 4 (2/3)x-1 + 5