In 53 60, begin with the graph of y = ex [Figure 31] and use transformations to graph each function. Determine the domain, range, and horizontal asymptote of each function.

MTH 132 - Lecture 23 - Graphing How to use f’ and f’’ to graph 1. Determine domain 2. X intercept a. Solve for f(x) = 0 if possible 3. Y intercept a. Solve for f(0) 4. Critical points a. When derivative f’(x) = 0 5. Increasing or decreasing on the interval f(x) 6. Inflection points 7. Concavity f” 8. Vertical and horizontal asymptotes. 9. Use combined information to graph. Example: ● x − 3x 1. Domain: (-infinity, infinity) 2. X intercept: a. x(x^2 -3) = 0 √ √ b. X1 = 0, x2 = 3, x3 = − 3 3. Y intercept: a. f(0) = 0 4. Critical Points: a. 3x^2 - 3 b. 3(x^2-1) c. (x+1)(x-1) d. Cr